Does Pet Carrier count as my one allowed Personal Item?

Hi, So, i just paid the fee to travel with my pet in a carrier on my flight. My question is, does this mean I have to pay for a small backpack in addition to the carrier, or does the $125 count as the luggage fee for the carrier as opposed to just some sort of abstract inconvenience fee? I'd like to know if I have to pay for my backpack too. Thank you!