I'll give you the easiest way. Dig a pit about 4" deep. DON'T dig where water will collect! Otherwise, you'll end up with a gravel-filled foundation that's filled w/water. Dig it 24" bigger than the outside dimensions of the playhouse. Line it w/filter fabric or landscape fabric, then border the inside of the foundation with 4x4 PT wood. Then, lay in the gravel, 2" at a time, and tamp with an hand-tamper. Make sure your 4x4 are rated for below-ground use. (I forget what the markings are on the wood in order to determine this.)
Then build your playhouse. WHen you're finished, I'd attach 4x4 PT 'runners' to the bottom every 16". (Well, put on along the bottom of each side, and go from there. 16" isn't written in stone ...) Of course, your child/children will have to 'step up' at least 4.5" + the thickness of the floor, to get in the house. If this is NOT OK, just build a step.
The main reason I suggest you dig the pit is because you won't have a settling problem. Plus, it allows for rain and run-off better than an on-ground house. The reason for the extra 24" is because when the water runs off the roof, it will hit the stone instead of the 'ground'. If it hits the ground, you get dirt and mud and 'ruts' along the eaves line. (It's just a mess.) Heck, if you think that later on you'd want a shed there, make the pit the size of the shed (+24" on all 4 sides), line it and fill it the same way, and you only do the job once! Gravel is sold by the cubic yard. Get a little extra. Just tell the Gravel Yard the dimensions of your pit and go from there.
I'm sure someone else will add to this. For now, enjoy your project. My best to ya and hope this helps.