Yes, if your pet backpack meets the airline’s pet policy for size (standard size allows up to 11″ for pet carrier height). Soft-sided is best for compressibility. Most Pet Backpacks will fit under the seat in front of your for flying with Dogs on Planes.
Airlines that allow Two Pets Per Person In-Cabin are: JSX, JetBlue, Chartered Air Travel, Alaska and Spirit. For Pet Travel with these airlines, you buy the seat next to yours and your Pet can either sit in the floor space, travel in the same carrier under the seat or on your lap.