"She is going..." is not passive but the continuous present tense.
"Elle va se brosser les cheveux" is the construction for a near future as "she is going to brush her hair" is the English construction for a near future.
The French sentence might look ambiguous, and you may wonder if she will first go somewhere and then brush her hair.
However, to avoid any ambiguity, if it were the latter case, the French would probably read: "Elle va là-bas (or other destination) pour se brosser les cheveux".
So, in the near future tense, "elle va se brosser les cheveux" best translates to "she is going to brush her hair" or "she will brush her hair".