Hi,I'm Miranda, and I'll be happy to help you with your question. I thought I'd offer my two cents along with my colleagues.
Of course, events, baby animals, hobbies, etc., are popular T-shirt choices, but that could be their fatal flaw. They've been done to death. Flea markets and stores are covered with them. I'm not saying that they aren't a good potential way to make money, but the problem is that everyone who makes T-shirts seems to do the exact same things.
If you want to do something different that will probably help yield some good profits, try something that will appeal to the alternative sub-cultures. I myself am a member of said alternative sub-cultures (I'm steampunk goth), and I can tell you for a fact that shirts playing to goths, steampunk lovers, punks, rockers, etc., will probably do very well. The reason I say this is because there are so few stores/vendors out there that have anything that a goth, etc., would find even remotely appealing (Hot Topic, Spencers, and that's about it unless your city is lucky enough to have a small business boutique that plays to this genre.). Honestly, you couldn't pay me to wear a shirt with a baby animal on it, unless it was a zombie kitten.
What you might try using for your T-shirts are things that are loved by these sub-cultures, such as zombies, vampires, anything steampunk, Day of the Dead interpretations, dark comedy sayings, pirates, magic, twisted fairy tales, etc. You could even try doing celebrities as my colleague mentioned (or non-celebrities), but make them zombies or even Day of the Dead.
I hope that answered your question. If you have further questions, please ask. It's been my pleasure helping you. Please remember to rate my answer positively, as rating me is the only way I receive payment/credit for my work. If you would like to request my help in the future, please post your question with "For Miranda Only" at the beginning, and I will respond.