Unless you've got a very valuable pet (in the financial sense) I can't see that there's any great risk of anything nasty happening.
Even if you were to provide your full name, address and telephone number, here on AB, it would be unlikely to result in any great problems unless you happen to have a stalker on here. (While a lot of people are now ex-directory, there are still vast lists of names, addresses and telephone numbers in the Phone Book. Simply knowing those details doesn't help thieves, stalkers and others with malicious intent very much. It's only when they also know that you've got three Van Goghs, two Botticellis and half a dozen Picassos, with no burglar alarm, that problems might arise!)