To give you an idea on my advice before i give it, i should mention I have a very large collection and specialize in Florida kingsnakes for over 20 years now (see my website www.bluerosy.com).
Ss long as he/she is growing feed it as much as it will eat and as often as it will eat. it will calm down after a couple months and won't try to eat your finger. The fact it is doing that means you should feed it.there is a saying we have for keepers..it's "listen to what the snake is telling you". if it has a feeding response to eat like that, up the food and frequency!!!
to give you an idea i feed growing Florida kings like yours every second or third day 9depending if they have digested the food item) and they will grow evry fast. this is healthy and will make for a stronger captuive with less health problems in the future.
Also make SURE you are using an undertank heat source so the snake can thermoregulate and digest it food bolus. An above heat sourse lamp/light bulb is not reccomended and will dehydrate the Florida king even more.
Also put a humidity box in the cage if you already don't have one. fill it with orchid moss or something similar. Florida kings dry out easily and do not get hybdrated properly from just a water ish.
you temp ranges in the unit should have a cold and hot spot. Hot on one end and cold on the other.
good luck!

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