There aren't stray dogs or cats running around Discedo, no. Once in a long while, usually in special item drops or events, we allow characters to receive typical pets such as those.

If you think Helen is up to it, she's more than welcome to try taming one of the monsters that currently reside in Discedo, such as those found on the Monster Wiki, or there are some "normal" animals, such as mountain lions, raccoon, crows, cockroaches (think pests and scavengers) that she could tame. If you plan to tame one of the monsters, make sure you run it by a mod.

Hope that helps!