I want to get my pet a job, but she doesn't have enough intelligence. Could someone tell me how to increase pet intelligence?

Reading books to your pet and there are a few intel boosters but for your purposes I would stick to books as there many affordable options. Note that a pet can only read unique books as in they can't read the same one multiple times

If your pet has very low int, you might want to consider playing Mystic Spindles. The game reward you with points you spend to either buy books or buy int directly. The cost to buy int directly gets much more expensive the more Int your pet has, so you want to use this option early, preferably before reading any books. Then as the cost gets higher use the points to buy books.