Advice on mounting a small pegboard above my doorframe (metal studs?)

Hi y’all, first time doing a mounting DIY like this, so I want to plan it properly before I drill anything.

I’m trying to mount a small vertical pegboard (about 1 ft tall by 0.5 ft wide, stocky, around 5 kg) on the wall above my doorframe so I can do hangs and pull-ups.

I found out a bit late that our building probably uses metal studs instead of wood. We’re in NJ, it’s a newer building, and I’m guessing steel for fire and flood reasons. I only have a basic stud finder, so I may drill a tiny pilot hole in the closet side to confirm.

The plan: mount a wooden board across the two studs I found above the door (photo attached), then bolt the pegboard into the board so the load spreads across the board and into the studs instead of sitting on one point. I’d use steel-stud screws into the studs, with toggle bolts as a backup.

Questions:

Is this enough to hold my weight?…