When you get exp from dungeons, your pet will gain them as well as long as you summon your pet before handing in the quest.

Kill mobs in Port Plunderer or (to be safe) in Grand Wildwoods near Port Plunderer entrance, from there you can gain exp as well as your pet.

Also make sure "Turn Off Experience Gain" from the general settings is not checked.

Ur wrote:

When you get exp from dungeons, your pet will gain them as well as long as you summon your pet before handing in the quest.

Yeh make sure your pet is summoned when you hand in quests - they get EXP from quests too.