I'd rather ask than get in trouble for not asking.

Are our pets allowed to have "relationships" with each other (my own pets, having a romantic relationship with each other)? (And of course, G-Rated.)

You mean like putting a character behind them? If so then yeah its ok, Plenty of people put characters to their pets XD (I'm one of them but i need to work on profiles) As long as what you stick in their profile is apropriate for the site (Pg-13) I can't think of a reason you'd get in trouble for them having a relationship like that.

Okay, thank you! I'm a neopian refugee, and I'm struggling to adjust to my newfound freedoms. There, your pets can barely be friends let alone have relationships with each other.

Yep. This is a PG-13 site, and RP romances between pets are certainly allowed. :)