If you are indicating that the dog chewed on the pool, was it the ring on the Intex pool or was it along the side walls or base?
You might get by with what others have said with the metal framed (regular or Ultra) Intex if the dog likes to "jump" up on the edge of the pool. Our German Shepard occasionally does that when the kids start squirting her with the water guns. However, if your dog is a digger or is chewing on the base/sides......then you will want a metal sided pool which will require a much higher investment but perhaps will be much better in the long run.
Many folks here on the Above Ground Pools sub-forum have purchased and set up their own metal sided AGPs. Get one of these pools and you are committed to leaving it up all year long, you prepared for that? You might, and I mean might be able to get into a 18 foot metal framed pool for 7 to 800.....maybe. Web search if you haven't already for a 24 foot round metal sided pool. Make sure you are sitting down.......when you go to these types of AGPs, you are going into serious pool ownership.
With my metal framed Intex pools I have, it's easy to be done with it at a moments notice with all this pool stuff, not so with a big, expensive metal sided pool. And for the record......looking at those metal sided pools.
Craigslist is an excellent way to pick up a pool on a budget. Just beware you may (and I would) need to replace the liner, but certainly the metal walls, ect should be good but still may need some attention before installed again. I most instances around here (think Oklahoma City metro area) I can find at least two pool for "free" if I come get them. It would be worth the time to grab some freinds and a pickup and get one of those.....
Bob E.