You can increase your pet's Strength and Defense by doing Fire and Water Faerie quests. Your pet can also eat Silver Knight Neggs and Power Neggs and Cool Neggs (only increase strength). Or if you are lucky you could get your pet's Strength or Defense raised by a random event! Training at the Training School on Mystery Island or at the Swashbuckling Academy will also raise your pets Strength or Defense. Just make sure you select the course in one of those.