Hello and welcome to the forum!
Congratulations on the first post!
You basically already answered your own question.
You did good preflop to raise 4BB + 1BB per limper with your KK. On the flop you have trash hand since A came up(BTW remember that A and K are common holdings of players on low limits and when one of those is your overcard on the flop you can easily muck your hand) and you should fold it to a raise.
When you are first to act you have to make continuation bet also when you have trash, but without knowing potsize, your stack size and who acted first I cannot give you more information about that.
EDIT: Ah, as I reread your post I see your stack size was 1.20 on the flop and if you were SB then you had to act first on the flop, so, presuming pot was ~1-1.15$ you should push directly all-in on the flop as continuation bet.