Fish in your fish tank, maybe but pets? On a war-time star ship? Hardly, at least in my opinion. I have a bad habit of thinking realistically, ok go ahead and say it..." It's Just a Game (tm)"... yes we know, so ask for ships with gambling on them and dress cloths and houses on worlds that you can visit on your 'days off'..but don't go back and read the introduction, or remember that you were given a ship under extreme conditions, it's a galactic war, and even Spock mentioned that it's so bad that the Federation might not survive.
If you ever got time off, it would be when your in for repairs after a big battle...oh wait...we self repair in space even from 10% hull..(chokes to think it)..but yes the ST universe could be great to live in, if it wasn't under certain destruction at the moment. I'd like to see more battles on our turf,not just fleet battles but fights where you get called to save oh, I don't know...a space dock from attack by Klingon attack ships. It doesn't have to be a fleet action, even a group of frigates that sneaked through the defenses, or birds of prey that cloaked to get there. Bring the war home to Earth, or the closest planets and make us fight for survival, not just time off.
OK, a K9 unit for away teams, like the targ for Klingon, that would actually help. But it would need a officer just for it, maybe make am officer just for away missions that specializes in animal backup, like the Klingon and the other enemys do. There might be other animals too from other planets we could 'level up' to as our animal trainer got higher levels. And an aquarium in the captains quarters to sit and stare at when your between fights might not be too bad, if your into that sort of thing...
I'd like to see (other) pets as well. It wouldn't be too much of a stretch (imo), considering Captain Archer took Porthos with him when they went after the Xindi. They didn't even know if they were coming back alive out of the Expanse.
Heck, even if we're in a war, I'll be damned if Starfleet tells me I can't bring my (insert choice of pet here) with me on my own ship! :p
"Fractal_Eye, the Admiral wants to see you in his office, something about insubordination...lol. And having a 12 foot alligator in your aquarium"...I already agree that animals for help on missions would be nice, so maybe they could be pets, but the Captains pet wouldn't be going on missions, I bet, so it might be considered 'dead weight' on a ship..where everything and everyone needs to carry their own weight day to day. The problem is, people see their ship as their private property, and not assigned to them. You don't own the ship, SF owns both of you..hehehe.