Other than the stuff that I would normally carry on a buddy dive, e.g., SMB, thumb reel, whistle (the big Storm one), strobe light and reflector and PLB, the only extra thing that you'd need is a fully independent air source. Since I'm carrying a DSLR with two strobes, I elect to mount my extra bottle on the side of my main tank and run the second stage where I'd normally put an octo. I use a long hose primary, so my backup second stage is necklaced and out of the way.
I did the SDI Solo course and they also recommend that you carry an extra mask which I do on occasion in a hip pocket that secures to my BC waistband with a strap around my left thigh.
BTW my camera rig is tethered to my BC d-ring so I can just let go of it in an emergency requiring both hands. I see a lot of photogs who don't tether and say they would never let go of their rig. Not realistic in a real emergency IMHO.
Most of my solo photo dives are shallow, less than 80' for sure. I'd start doing solo real shallow until you become comfortable alone. It takes a while.