Wiki - Pets with Packs
Some pets have backpacks and will let you store items on them. Others have loot on them when tamed, but no pack.
Pet packs can hold 1600 stones or 125 items, whatever comes first. The Strength of the pet has no effect on it's carry capacity.
If you attempt to use a Pet Leash on a pet that has something in it's pack you will receive a message that emptying it's pack is required first. If the pet has a pack then simply remove the items. If not, the 'drop' pet command will have the pet drop anything in it's pack at it's feet. Releasing the pet will also have it drop the items at it's feet and allow players to retame the same creature with an empty pack, thus allowing Leashes to work.