I always extend and follow the same rules for my son as I do for me. I just think it is respectful to do so but also I worry about any future implications not following rules could carry as I like to come to Thailand often so I'd prefer to do things right despite him not necessarily needing it. Everyone says it depends on the immigration officer on the day when you do different things and last thing I'd want is questions galore around this or it to even impact my son or me returning or it affecting my ability to get a longer term visa at a future date.
It's done same day Tahnee. Koh Tao immigration office usually really quick at getting everything done. You do need the proof of where you're staying though from the hotel/hostel