I plan to travel with Peach from Kix to arrive Incheon at 09:35 and catch Vietjet flight departing Incheon at 11:40.
I have no check in baggage. Is it doable?
It's possible to do an airside transit at Incheon airport which is fast and you can do that on seperate tickets. Vietjet doesn't have a transit desk there as far as I know but they offer web checkin for ICN departures so you should be able to get a boarding pass. Both airlines use the satellite terminal where it's possible to go through transit security without taking the train to the main terminal but watch out to not accidentally do so. You will need to show your boarding pass or reservation at the security checkpoint. Transit experience is pretty smooth and you have plenty of time.
If you need to go through immigration it seems still doable if the flight is on-time but risky. I waited in line for more than 60 minutes there and you need to take the train between the terminals which takes up to 15 minutes each way. As you don't have checked bagge there is no reason to use that route.