Not to worry, it will be fine. Before watering anything, stick a finger or two down into the soil about two or three inches to see if the soil is dry.
It should be ok. Be aware the high sphagnum content will hold lots of water, overwatering could be the death of your lime. Sheeoot, florida, you can grow anything. I'd put the little beauty in the ground. *wondering* are there male and female key limes or do they self polinate, hmmm.