If you're flying on Korean Air one itinerary and paid ticket - they will give overnight hotel. Have to call customer service and ask. Also, if you are flying Korean Air both flights, they'll give you both boarding passes and check your bags all the way through. Don't have to collect anything.
So if that's the case, IMO, you don't have to be at the new airport until 9ish. T2 is VERY empty at that hour. I recently flew out at 10 AM and we arrive to the airport at like 8:30. Security took SECONDS, nobody in line.