What chav connotations? Until this thread, I'd never read or heard a negative comment about Tara. It's too unusual. Even in Ireland it's one of those names like Clodagh and Maeve, more popular with ladies who play bridge. It's not a very common name even in Ireland.
Sharon and Tracy type names would be names that were extremely popular and 'new' late 60s and early 70s. I would say perhaps Dawn might be in that category. I have a lovely friend with one of those names.
I don't care about the Dog thing! I like Polly and Bruno and Sadie. IMO Tara doesn't work on a dog. It's like Anna. Too modest for a dog. Not cutesy enough.
OP, good choice imo, I only know one Tara of any age in real life.