Solid advice from everyone so far. The PC is the most dangerous place for sure, but if your account looks good and the UC isn't a super high tier I doubt people will look into it.
What I will say is, if you do decide to ever trade the pets, stalk the PC for a good while to see who's who. There are some people who are "high-profile" PCers and are always on there, and I'd be more wary to trade with them because suddenly that pet would be in the spotlight, too. And of course, there are some people you should just never trade with because they'll report their own pet to see if it's "legit" or not.