I've heard around that toady has specifically stated that he doesn't want Urine/feces. I'm not sure if that extends to animals or not, but that could be why. The other possible reason is that animal droppings don't burn hot enough to smelt any of the metals we use in dwarf fortress and there's nothing else that currently uses fuel yet.
Toady has carefully not taken a position in the feces debate. I've seen people claim that he did many times, but none could refer me to an actual place where he took one.
I can offer you some actual places! The quote is from a general set of frequently asked questions, covering stuff from multithreading to graphics. It also includes a link to a Q&A recording with Toady at the bottom. As it notes, Toady is not personally against it - it's an integral reason for the existence of sewers. However... the bad press may be nasty.
(Also, we should probably move on from discussing this - if it goes for /too/ long the threads tend to get locked or way too derailed)
11. This game is so realistic, but sex/feces and urine/certain other intimate bodily functions are conspicuously absent. Are there any plans to add these later? Because it would really add a new dimension of realism/difficulty/etc. to the game.
These two features come up often, and the explanation for why is similar for both, but with some minor differences.
While Toady doesn't have an issue with including sex in the game, he feels that the negative publicity and reception it would bring is not worth the payoff; the game has enough potential for brutality and violence in it without adding the extremely controversial aspect of rape gameplay.
Urine and feces, like sex, isn't something Toady has a personal objection to either. He feels that animal droppings and fertilizer are an important aspect of a realistic world, and that sewers are a classic adventuring staple. However, he has stated that the game will likely include excretions up to (but excluding) dwarves, out of a desire to avoid becoming (to paraphrase) "that game with the pissing and shitting and raping dwarves". The concern is that the payoff from adding these features would not be worth the lost fanbase and bad publicity and tarnished reputation it would bring to the game.
Toady has said that, as the game grows and develops it is possible that this could change, but for now it's an issue that can be handled by the modding community for those who really want it.
A discussion of this can be found between 24 and 30 of this Q&A recording located here
But anyway - it's as I thought - peat just doesn't burn hot enough for smelting. However, it works fantastically for internal heating, which I suspect will rock up in the next decade or so. Burning peat apparently smells rather nice, too... or at least fragrant. I wouldn't know, since the amount of peat in Australia would probably be measured in units of "What the hell is peat?"
I could see peat being used as a source for stone material, too - if the peat is allowed to dry out properly it makes a good building material. Carving, not so much - but sod houses are a real thing and small peasant villages near bogs would certainly use it.