I'm guilty of this, though it's more for fun than for any serious photography.

GoPro is actually releasing their long anticipated Karma drone on Monday, 9/19/16.

There's a number of preview videos out there, but they've been pretty tight lipped about releasing much on them.
It's supposed to be a very quiet and smooth platform, and it may be the perfect fit for you as far as re-using GoPro camera.

There are other options with GoPro mounts on them, but they are typically more expensive (over $1k).

As far as standalone drones, I'm using the Autel X-Star Premium, and for $899 retail I have not seen a better option.
It is very similar to the DJI Phantom 3, but with longer range, better controller, and better software as well as 4K video.
It comes with a RTF kit that includes the case, spare parts, room for extra batteries, and more; a total solution.
It will fly unattended via GPS (i.e plan a route on the map and let it go), but is very easy to fly manually as well.
Camera controls include remote exposure settings and pretty much anything you might need to take a great pic.

We've had this thing over a mile and a quarter away and back, and batteries last longer than a lot of the competitors.
Video is amazing, and the image stabilization gives you great smooth images. Customer service has also been great.

Once you get into the $1500+ category, you get into serious drones with larger payload capacities, such as being able
to carry an SLR and heavier video equipment, but honestly the 4K video I've gotten is very good at ~$800 complete.