I would say どうして「土曜日は働きますか」ではなく「土曜日働きますか」なんですか? or どうして「土曜日」の後に「は」が入らないんですか? along your original.
As for your question, particles に or は is not necessary for days of the week. 土曜日は働きますか is not wrong, but は performs as a contrastive marker in this sentence, so it has a nuance, for instance, "I know you don't work on Sunday, but how about on Saturday?"