It's absolutely worth applying if you want to be a vet, as long as you meet the criteria there is no reason you wouldn't have a chance and you seem to be aware of the pitfalls of graduate entry in terms of the finance.
Volunteering in animal shelters and zoos is a good start but since you will need to do some more work experience before applying, I would suggest starting with some vet practices to make sure it is actually what you want before going any further!