Sure, as long as pets are well groomed and pet soiling is minimal or resolved immediately. Today many manufacturers make stain and odor resistant pad and carpet. We will always recommend looking into one of these products if you have pets. Your Lowe's Flooring Specialist should be able to help you choose which one is right for you. Just be upfront with them about how much abuse your carpet will take from your pet.
When it comes to carpeting and pets, a cut pile is the better choice. Looped pile carpets can snag on pets’ nails, causing yarn to fray, tear or pull out. Looped piles can also be a chewing temptation for some pets.
Tile is a great alternative if you have destructive pets. Tile is a hard surface that can easily be cleaned and your pets (usually) will not damage it.