Unlike poultry, crundles and alligators do not work; as the two produce scales there is no leather to be had - unless you've modded your game, though in that case one might also use the mod that gives more leather for larger animals.
Reading earlier, I suppose dfhack's autobutcher could use an update so that it has the option to not butcher creatures too small to give a skin (or horn or gizzard stone, if going for those). This would allow one to only get skin/2 [bones]fat/2 meat/1 skull outputs.
Also, I'll note the estimated required size is bit higher than 1200-1400, I think around 1800? Exact value depends on animal due butchering looking internally at each part separately(E: A look at turkey raws and using
butcher-science gives min size somewhere between 1643 and 1735, with 1689 average by my calcs, though Sphalerite gets 1587 for 'birds'; E2: And now I remember (and confirm) that keas sometimes produce 2 meat on butchering too, despite avg 1000 body size), then summing together. With that, Turkeys are big enough in just under three seasons, not four, which means they can outcompete peafowl (with under two seasons), if you're willing to make more butchers and accept the butchering date moving season earlier each year.
E: Oh yeah, in regards to PatrikLundell's "normal case": instead of splattering, telefragmenting the animals with minecarts is more efficient. Put the animals in a cage, put cage in a minecart, accelerate minecart to over 1 tile/step, make it expel the cage at speed with wall at the tile the flying cage would have skipped through. Cage and upperbody end up on the minecart side of the wall, every body part ends up 1 tile on the other side with zero velocity, combat reports or harm to dwarves standing right there.
2x4-square impulse accelerator with pressure plate triggered by cart linked to a floodgate to release the cart into wall is enough for this, iirc.