If you will be driving your own car (one that you rent or borrow) then it will be worth taking a car seat with you and placing it in the car. But, if you will be depending on public transportation, then take the seat for the plane ride and leave it in the hotel the rest of the time. It will be too much of a pain to lug it around all over the place. When our daughter was 6 months, we went to Korea and we did not bring her car seat. When she was 2.5 years, we brought her car seat with us to Korea and it gave me some peace of mind (we were borrowing a family members' car the entire time we were there).

Just use your judgement. If you will be staying in Seoul, do take advantage of the wonderful subway system. It will take you anywhere you need to go. And, the buses there are quite convenient. Taxies are cheap and, generally, fast, but you're taking more of a risk. People drive pretty crazily. We rode in taxis without incident, but I preferred the subway. Plus, when she was a toddler, our daughter loved the subway.

Hope this helps. Happy travels! Hilary