If your parents have already said no I really wouldn't advise just doing it anyway. Unless you absolutely know that they wouldn't really be upset and wouldn't insist you find another home or the pound for her.

And people think of dogs as living toys. The kids play with 'em and then the kids get older and bored and the dog becomes a nuisance that is always underfoot and suddenly has medical needs! Now it's not a fun toy anymore, but an annoying burden that snores and has arthritis and we're moving and it would be bothersome to take that old bundle. We'll get a cute little puppy when we move to the new house! Oh, a new puppy would be so fun! We could play ball with it and teach it to bring the newspaper!
So long, old snoring lump that gets in the way when I'm cooking dinner and who bores the kids.

That is how people think.

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"You gotta help us, Doc. We've tried nothin' and we're all out of ideas!"