I've found this model from Dima Tsvetkov on Thingiverse and adapted it for the Barbie-size. The original model has a 1:12 scale. The files here are the original ones, so they are to small for Barbie.
I scaled it up by 220 % to make it suitable for 30 cm dolls. Scale it as you like.
The print is quite easy. I printed the complete stool in PLA, seating surface downwards. Bigger prints of the complete model (like the 220 % scale) need supports on the print bed. For more stability I recommend an infill of at least 25 % so that the legs hold up.
The user re-uploaded this model. The user is not the original author of the model.