About this quote from Harry Potter And The Sorcerer's Stone:
He understood what he had to do all right, it was doing it that was going to be the problem.
I think that it is better to add a conjunction between the two clauses to make it correct in grammar.
He understood what he had to do all right, (and/but) it was doing it that was going to be the problem.
The second part is an afterthought to the first thought. A semicolon would put too much of a pause and disconnect two thoughts that are closely intertwined. It's fiction, where punctuation is more fluid, especially when a character's thought is being narrated.
Did it have a comma in the original? Maybe that's British grammar instead of American grammar.
In American English; that sentence would use a semicolon and not need a conjunction (and also a comma before "all right" because it's a type of parenthetical comment) because the phrase after the semicolon directly relates to the first phrase.
It wouldn't necessarily make the sentence grammatically incorrect to add the conjunction "but"; however, it would make the sentence a bit more awkward with some unnecessary words. If you wanted to add one, though, it would be read better to say, "He understood what he had to do, all right, but doing it was going to be the problem."
