Trading in Pet Simulator 1 was introduced in the 8/16/18 update. It allows you to trade any of your pets with others, or give them away for free. You must have at least 2 pets to be allowed to trade, due to being able to trade away your only pet for free.
Steps[]
Select the Trading button on the side menu. There, a list of players with trading enabled will show. You can request a trade by clicking/tapping on their name.