I was able to lift a Sony Nex 5n using:
DIY Xaircraft flat hexa frame
Avroto motors, 30 amp esc
Helibest 2 axis camera gimbal (cnchelicopter.com)
Foxtech Horyzon FPV camera
200 mw 5.8 video/audio transmitter and 1 x 6000 3s mah lipo battery
APC 10x4.7 props
DJI WKM
I had a flight time of 5 minutes under that load. I was carrying a lot of weight, but the craft performed without issue. It was actually flawless until I decided to get fancy and bought expensive full carbon fiber props for my craft. One of those props snapped in flight wrecking my bird (another story: Just stick with APC or Graupner props).
I don't see why a DJI F550 couldn't lift a Sony Nex 5n with stronger motors and a decent camera gimbal. I didn't just want to carry a Gopro camera. You want to have options. It a go pro is all that you intend on carrying you can stick with a quad and have less weight, get more flight time, and transportability. The Helibest camera gimbal isn't cheap, but I used it to carry my Sony Nex 5n to take pictures. It worked for me.
I ordered another gimbal since my last one was destroyed after a crash. It works well enough to get nice still photos (You'll need a camera with image stabilization for best results). My Gopro video were vibration free.
I have Aeroxcraft's landing gear. I just wonder if I'll have enough ground clearance for the Helibest camera gimbal without making any changes to the thickness of the foam for the camera mount. My current set up is on a Y6.