I would just use two brackets and mount one with clamping hollow-wall anchors. Double drywall is plenty strong for the light half of these loads. There are several types which take a 3/8" (~10mm) hole and hold quite firmly. No need to reinvent any wheels.
That said, yes, your solution could work. A single toggle bolt at the top of the bracket would theoretically support the entire thing (though you'd want two to prevent spin). The shelf keeps the bracket from swiveling sideways. The critical aspect would be keeping the shelf firmly attached to the bracket so it can't flip off. There will be substantial cantilever.