What was the name of the fort that Washington set up during his first campaign against Fort Duquesne?

Fort Necessity is the correct answer.

Explanation:

In his first campaign against Fort Duquesne, George Washington encouraged his men to build Fort Necessity to prevent a counterattack by French and Indians. Previously, he had led the construction of a campsite in the area, in order to gather the necessary resources to continue with the campaign. He accomplished this task with Tanacharison and the Seneca tribe.