Nope, it used to be, a fair while ago, but they stopped it =3
Well. Technically you still pretty much can.
Like if you pound a pet, then your friend adopts it, and then your friend pounds a pet, and then you adopt it. There's no specific trading facility/page though. As long as both users consent and there isn't a payment or exchange of sP, I'm pretty sure there's nothing wrong with it.
I didn't think you could actually say "Trading ___" or ask to trade pets though?
"The selling, buying and trading of pets is NOT allowed. This violates Subeta's rules and any attempts at doing such will result in disciplinary action. "
Read the sticky with the rules at the top of the forum. :D But, if you and another person decide to trade without using the boards, then, I don't see how you could get caught trading. :D It's best not to, though.
Trading pets is NOT allowed. You can find the mentioned rules HERE.