This can be a very lucrative field if you approach it correctly. "Pet" itself can be a pretty big niche and also pretty competitive, but still possible. There are all kinds of offers available on networks. Just a quick glance and I see pet prescriptions, dog toys, pet pendants, cat training, dog training, free cat litter, free shampoo, petco vs petsmart payout, vitamins, etc. You may consider a subniche in pets like dog training. May be easier to promote through SEO and PPC with less competitive keywords
If you are serious about an affiliation with any product, you are going to need to build a list of customers. Finding a product is easy, the money is in your opt-in list.