Do your construction plans allow for any insulation?
Bear in mind that a little insulation is way better than no insulation at all.
Even working with a tight budget, minimal wall and roof insulation will make a major reduction in cooling requirements, and thus a likewise reduction in energy costs.
Site the building and windows to reduce solar load from the south/southwest. If to be used primarily in the summer months, consider white or light exterior colors to reflect as much heat as possible. Perhaps even provide some window awnings to reduce the solar load.
Rather than a low window location for the AC unit, could you place the unit higher in the building to blow (high) into the loft, and encourage return flow (low) from the main floor area. Try to encourage a "loop" airflow pattern.
Will the playhouse be shaded by trees or adjacent buildings? How are you "sizing" the window AC unit? Will you provide a vapor barrier? Do you have plans to properly seal the floor plate, windows, etc. to prevent infiltration?
By utilizing proper construction methods and standards you should be able to build a relatively efficient structure. Take too many shortcuts, and well...
as always, offered only as opinion
