Either choice is fine. It is never strictly necessary to use the past perfect; it is just a nicer style (when used correctly); it adds a touch of eloquence to the sentence.
Not all native English speaker utilize the past perfect, at least not in every conceivable situation when they could do so.
The important lesson here is that you can use the past perfect in that situation.
As a learner of English, you must learn about the past perfect and when it may be used and why. You will never go wrong if you don't use it (just less sophisticated); but it can be inappropriately and awkwardly used.
Why we can say:
Tony hadn't wanted children until his daughter was born.
is that we have two clauses:
S1 until S2
S2 is in the past ("his daughter was born"). S1 is also in the past: moreover, it is in an earlier past than S2. The "until" word clearly places it there: S2 is in the past, and there is a causal relationship between S1 and S2 such that S1 is before S2. Therefore it is legitimate to use this "past before past" English construction: the past perfect.
The meaning is still clear if the simple past is used for both clauses, and no rule is broken.