Transporting livestock in space

Yes, we humans evolved to eat meat... vegetarianism is a self-imposed dietary impoverishment. The romance of space travel would not compensate for the gloom of compulsory abstinence from meat.
Maybe not for you - but I strongly suspect that you would have all the qualified volunteers you needed.
I think animal husbandry is far too inefficient regarding cost/effort/volume/weight/etc and that hydroponic GM plants would be far more efficient (you could eat everything, and they reconvert exhaled CO2 into food) and produce all nutrients complete with appropriate tastes/textures/etc.
Eventually, though, permanent offworld colonies will want to provide a truly Earthlike environment - either in sealed artificial habitats, or on terraformed planets. That will have to include animals, including non-domestic animals.

Even a self-contained space habitat, like the one in Spidergoat's picture, could contains parks and zoos, maybe small wilderness patches.