According to the Constitution:
"If any district Senate seat becomes vacant, a special election shall be held within one week to fill in the vacancy."
This would seem to suggest the election should be held next weekend. But, there is some leeway, since Texasgurl has indicated her resignation would not be effective until AFTER the special election.
I believe it is the function of the Secretary of Forum Affairs to set up elections. That post is vacant until Gustaf takes office and appoints his cabinet.
As he pointed out, we cannot hold an election until AFTER she resigns.