Sol95 is right. It will be easy.

The airport express train (AREX) commuter line is one option. Fast and inexpensive. Downside is that you will have to do some walking to get to/from the train platform, both at ICN and also at GMP. If you have lots of luggage, this becomes a bit of a pain.

I think the easiest way is to take one of the Limo bus.Link here. It will take you directly to the departure terminal. You just pay for the ticket and relax on the bus. Might even be able to see a bit of Seoul on the way there. The only difference between the standard and deluxe bus is that the standard has a 2-2 seat arrangement and the deluxe has a 2-1 seat arrangement. Deluxe is pretty darn nice for a bus! If it is your honeymoon, I would spend the extra $2 per person for the deluxe. But if time is a factor, just take the next one available.

No need to book the bus in advance. Maybe just have some Korean Won cash available to pay for the ticket.