In one approach at least, you can simply say that the clause is the complement of doubt, just as you would say that it was the complement of doubt if the latter was a verb.
Notice that it is in some sense part of the argument structure of the noun doubt that it can select a clause. Or in other words, you can't readily apply the same structure to any old noun: *the book that the universe is large, *his tolerance that Mary is rude. There's a property specifically of the word doubt (and some other nouns) that "licenses" the clause.
The term apposition is usually reserved for a much more general structure where you're implying that one phrase "equates" to another, but where the first doesn't necessarily "select" or "license" the second as such.