Only campgrounds and 'developed' recreation areas are closed. The rest of Tonto is open.
Since the QV shooting area is not a campground or a developed area it should be open, just practice social distancing.
https://www.azcentral.com/story/travel/arizona/road-trips/2020/03/24/arizona-national-forest-campgrounds-closed-coronavirus-prescott-coconino-tonto-apache-sitgreaves/2904703001/