I haven't calculated the material cost, but it's important to note that the cabin isn't complete without adding the cost for the foundation, roofing felt, metal sheets, and paint. And if you want the cabin to look like the picture, you should also add the cost of the roof tiles.
When it came time for a playhouse at home, I threw one together using pallets. The period during which the playhouse is interesting is not very long, so in hindsight, instead of a playhouse, I would have built a shed instead, where a smaller part could be used as a playhouse. With its own entrance and window.