I'm guessing it would have to be done before the next lot are handed out. Maybe after Wimbles? Would be an ideal time to do it.
It would, or at the end of the season. I'll try to check when the next one is. I think Queenie is in Scotland for her annual holiday, but most of the time these days she leaves it to one of the other royals to do it anyway, usually Prince Charles. In theory the New Year honours are supposed to be awarded before the Birthday ones are, but if you remember, in 2013 he didn't pick his OBE up until October.
PS - All I can find is that the last one was on 16 June, but they do have around 20 each year, which is more than I thought,