"It was an ambulance that took an injured dog to a vet." Or : "It was the ambulance that took the injured dog to the vet."
Are both sentences, grammatically spoken, correct? Which sentence is preferable? Or does it depend on the situation?
The structure of the sentence (a cleft sentence) is not very natural, however.
Probably your reader already heard something about "the" dog, and even though we may not mean a specific doctor, we tend to say "the" doctor, so (although I agree with Mike that the particular circumstances might make other articles more appropriate), probably "An ambulance took the injured dog to the vet."