KQo in BB hates the min-raise

You don't have enough chips to get away from this hand in my opinion. If you fold here you'll be left with 1550. If you double up you'll have 4900. Especially since he has limped in before with the blinds that high. You can't put him on a big pair like that. This situation reminded me a lot of a hand in HOH volume 1. I don't remember the page but I do remember that the hero had QQ w/ a K showing on board and Harrington strongly believed in calling an all-in raise against his opponent due to the inflection points of his stack. Check out this problem, it may help with your thinking in this spot. I think your in that situation as well since your opponent's range is wider than a big pair and who limps w/ AK in EP? Hands that could be putting you to the test that you are ahead of or equal to are KQ,KJ,KT and any medium pairs that make second pairs to the board.