I have to agree with Sea Tyger- after every modern war, the Navy was invariably punished for having won it. Force levels, new construction, and even R&D are invariably cut as spending priorities (and fickle public opinion) are turned toward more "domestic" priorities.
There's an old adage:
"God and the Navy we adore,
In times of danger, not before.
The danger past, all is requited,
God is forgotten, and the Navy slighted."
It would be little different in the post-War Federation.
The closest real-life analog we'll find to the Dominion War is, of course, World War II. During the War, multi-million dollar (multi-billion or even trillion dollar in today's terms) construction programs were the order of the day.
At one point, American shipyards were commissioning new freighters on a daily (and sometimes hourly) basis and a new destroyer once every three-to-five days.
Spending on ships, aircraft, tanks and bullets was profligate, if not wasteful. All that ended and fiscal priorities were turned upside down within hours of the Japanese surrender and the end of the War.
Within two years of the conclusion of hostilities, the Navy had dropped its overall force levels by fifty percent, and over the next ten years dropped total man power levels by something approaching eighty percent. They decommissioned something like ninety percent of the carriers, sixty percent of the battleships, and approximately 2/3rds of the destroyers/escorts.
There were serious proposals in Congress and other halls of power to cut the Navy down to seventy ships (smaller than the current Coast Guard) and a single carrier and to disband the Marine Corp entirely.
Much of this stupidity was pushed by the newly-independent United States Air Farce and the absolutely assinine notion (you were an arrogant ass Curtis LeMay) that conventional warfare was no longer possible because we'd just nuke anyone who pissed us off.
Only the "Revolt of the Admirals", the Russian acquisition of atomic arms, and the Korean War prevented a cataclysmic and disastrous dismantling of the American military. Overall military budgets were slashed by fifty percent or more from pre-war levels and by eighty percent or more from war-time highs.
Overall force levels (except for the Air Farce) were cut in half or more.
If memory serves, it was twelve years or more before a new class of ship appeared in the U.S. Navy- and force levels were being drastically reduced all the while.
Most "construction" in the naval yards in the late forties, fifties, and early sixties were experimental- trying to retrofit the existing fleet to handle newly developed jet aircraft and guided missile technologies.
I can't think of a single "modern" warship that put to sea in the late forties or fifties, that wasn't either a conversion of an existing design, or a cheaper, less-capable "austerity" measure designed to cut costs in a rapidly shrinking and competitive budget environment.
The first purpose-built guided missile destroyers didn't appear till the late sixties- all the rest were conversions. The first purpose built "super carrier", the Forrestal, wasn't laid down until the mid-fifties, and that only because it was an absolute necessity- the older Essex and Midway class carriers were having more and more trouble keeping up with new aircraft designs.
The post-Dominion War Federation would be no different. Even in a "moneyless" command-and-control society, resource allocations would shift dramatically from rebuilding the Fleet (and R&D for the same) to civilian reconstruction and rebuilding efforts and to consumer goods.
A war-weary population with a large percentage of skilled veterans would shift away from an at-war footing, to a less austere, more "living the good-life" mentality- just as we saw in the late 40's and 50's in Americana.
The size of the fleet would be cut dramatically, recruiting efforts would drop off dramatically (and military service would seem far less glamarous). Because of the need for fewer men and a higher percentage of trained veterans, entry requirements would be tightened considerably as well.
Given that there are no major threats on the Federation's horizon, and that the existing force-structure (thanks to the PDI) appears to adequately meet the fleet's existing priorities, new construction and R&D- including new ship designs- would taper off significantly.
New starship construction of starships would be just sufficient to restore the fleet to pre-war levels and to meet a very limited growth margin- no more.
There are no new technological hurdles that the fleet needs to meet (such as jet aircraft or guided missiles), so there's no driving need for major innovation or upgrades to the fleet -and therefore, no need to invest resources (money) on new starships. There is no new "arms race"- the Federation is not competing with the Klingons or the Romulans to see who can field new vessels faster. There's neither the need nor the inclination to turn out new designs at a rapid pace.
Very elderly vessels, those with major flaws, or which are otherwise difficult or expensive to maintain and operate will all be retired and then sold or scrapped. Those vessels which are relatively new, and gave good service, but which are not needed will be decommissioned and moth-balled (placed in storage in case they're needed in the future). Even new vessels judged too expensive to repair will be decommissioned and scrapped (the fate of the brand-new U.S.S. Franklin CV-13).
Smaller vessels that can be turned to civilian uses will be sold off at firesale prices as the Federation seeks to retire some of the massive debt incurred in wartime spending, and we're liable to see a lot of Mirandas and smaller vessels disarmed and converted to civilan freighters. We're liable to see a number of Federation designs converted to civilian research and economic applications (Jacques Cousteau's beloved research vessel Calypso was a converted Navy mine-hunter during the War).
The first decade or so after the Dominion War will be one of rest, repair, and austerity for the Service. The only "new" designs would either be those which meet a specific shortcoming in the force structure or be the completion of vessels begun during the war- a matter of "clearing the decks" as it were.
For a few months I have been working in a fan supplement that will include lots of new starships (as well as starship weapons, shields, maneuvers) for the biggest powers in the Star Trek galaxy. I think that in times of war weapon industry and research become a priority and thus by the end of the conflict there were a lot of advances.
During the post-War drawdown, work on new designs and new weapons systems begun during the war would be completed. Once that work is finished, however, new vessels and new weapons designs would be few and far between.
A good rule of thumb is that anything that would take less than eighteen months to finish would be completed, while anything taking more than eighteen months would likely be cancelled outright- unless it filled a pressing need.
Shipyards themselves will be laying off workers and decommissioning dock areas as the need for new vessels tapers off, and a lot of the "brain trust" in these industries will be shifting to civilian, rather than military applications.
No- for at least a decade after the War, new starship designs would be rare and new vessels few in number. Those that do reach completion would simply be modifications of existing designs and therefore "variations on a theme".