Upvote:4
Korean Air has a table of transfer times / minimum connection times on their site.
Considering you have an international (Incheon) to international (Gimpo) transfer, their site oddly doesn't cover this, but does cover International flight (Incheon Airport) > Domestic flight (Gimpo Airport), which has a minimum connection time of 150 minutes. Give you're going international, that's at least another 20 minutes if you're lucky, but even ignoring that, 150 minutes is more than your current gap of 110 minutes.
Short answer: You need at least 2.5 hours.