How old do you have to be to take ownership of a pet?

I'm 15 years old, and I have a cat that's almost a year old. We still haven't gotten him to a vet, and I'd really like to get him to a vet soon, because I love this cat, but the problem is, I don't think my dad would let me. We're low on money and we have A LOT of cats, and plus he wouldn't wanna have to tag along for my cats appointments. The reason I want to know how old you have to be is because, I want to be labeled as the owner,and I wanted to know if I could take the cat to the vet on my own.