I agree with Tessa, and her good-humored response makes me smile. Yes, sentence 1) would make Miss Dare a born-again person.
There is another way, too, to state this:
Virginia Dare was the first-born English baby in America.
Personally, though, I prefer Moon's second sentence, which is simple, clear, and straightforward. In the second sentence, 'first' modifies 'baby,' which is logical and correct. But in the first sentence, 'first' modifies 'born,' which is illogical.