Okay, so your child was the one who wanted the new pet. Your child was also the one who chose the new pet. However, this does not mean the sole responsibility of the pet lies with the child. The new pet has become part of the family, so it is the whole family’s responsibility.
Before you get your new pet, sit down with your child and make clear the rules and obligations that are expected of the child. Make sure the child is aware of how much food the pet will need. Give the child rewards for meeting those obligations, and punishments if the child neglects the new pet, for example no more TV.
However, you must also remember that there are going to be times when the child is simply unable to take care of the pet. For example, if the child is ill then they won’t be able to take care of it. Also, if they have a lot of homework to do, you can cut them a bit of slack then too, and this will be the time for you to step in and help out with the care of the pet.
But it doesn’t matter how much the child takes the pet care responsibilities seriously, you have to accept that the financial obligations will rest with you. You will need to pay for the food, the vet’s bills, and any other costs which may need to be met. That is, of course, unless you plan to send your child out to get themselves a job!