The correct completion of the sentence with time clauses is:
"I will vacuum the carpets while you are doing the ironing."
Here, "while" indicates that two activities are happening simultaneously.
If you want to use "since," the sentence would change slightly, for example:
"I have vacuumed the carpets since you started doing the ironing."
In this case, "since" indicates that the action of vacuuming has been ongoing from the point when the ironing started.