You can upgrade your pet in the mobile app "Grub Guardian". It is a fun mobile game which you use your W101 account to train your pets in a tower defense styled game.
To add to Gallaer's post...you can also win exclusive housing items, elixirs, packs etc from Grub Guardian. There are different settings (easy to use toggle) that determine if you're using it for training the pet or winning prizes...so after you've done your pet training you could do some extra ones for those too (I think it is up to 25 times per day for prizes)
Just go to freeKIgames.com and look for Grub Guardian (under Strategy Games, then Tower Defense games). As Gallaer said, there is a mobile app for it if you want to do it on-the-go
