I should think she will. Edward and Sophie were given a lesser title than usual wehen they married and it was announced then I think that their children would not use the titles of Prince etc.. but just Viscount and Lady. I don't believe it was intended that Ed and S would be doing much royal wrok, that only came later and clearly they preferred it if their children did not have the titles of Prince and Princess as they were so far down the Line and they would problaby never be needed for Royal duties. But Harry, in due course will be the second son of the King and brother to the next king. His children will be higher up in the line and he and his wife WILL be doing royal duties. So I would be fairly sure that the queen will want his children to be prince and princess and that Harry will want it too. I don't know about Meghan.. but I would imagine that she will agree.