Storage heaters tend to be very heavy - summerhouse walls and plasterboard tend to be somewhat weak.
Perhaps a horizontal wooden batten or board screwed firmly across a couple of existing uprights will provide a more secure fixing.
But the concept of a storage heater in a summerhouse seems bizarre - you will lose a lot of heat and needlessly waste money unless you insulate walls and ceiling.
Good luck...
Peccavi
March 2010