Many get involved with quadcopter drones with the goal of conducting aerial video, or first person view (FPV) flying. Many of those same people rush out and purchase relatively expensive equipment for this purpose, without having any quadcopter flying experience. I think the plan is to learn how to fly using this same expensive equipment. But crashing a quadcopter is an essential part of the flying learning experience. Thus many lose that expensive equipment within the first few flights, either crashing/ruining their quadcopter. Or simply their quadcopter flies away never to be seen again.
I STRONGLY recommend some patience before attempting aerial video, or purchasing a mid to high-end quadcopter. Spend a few weeks learning to fly a cheap (~$30 to $40) toy quad first. Don't let the low price fool you. These cheap quadcopters fly very well (please see this video). They are an excellent way to learn to fly, much better than simulator software. A cheap quad will more than pay for itself avoiding that first crash of an expensive rig. Once you notice that you're not crashing as much, then consider purchasing the following $7 pocket camera. Many just tape this cheap camera to their training quadcopter for their first foray into aerial video. Although the resolution is only 720 x 480, the video is not too shabby from this camera.
But if you want something a little more polished, consider the following 6-axis quadcopter with a built-in, automatically and remotely controlled camera. Resolution is also only 720 x 480. But the frame rate of the camera more than makes up for it at 60 frame per second. Cost is about $65 ready to fly. If you purchase this as your first training quadcopter, consider unplugging and removing the camera for those early training flights. That way the camera will be in good condition when you're really ready to use it. Here is a link for more information, and a couple sample videos taken with my own V222.
But if you have your heart set on sending your GoPro skyward to get true HD video, you're going to need something bigger. Maybe consider the following mid-sized 6-axis quadcopter? About $83 ready to fly:
But before you risk that expensive GoPro in aerial video, consider the following much cheaper 1280 x 720p HD alternative. About $48 total:
And again here's a sample of my Mobius attached to my WLToys V262 quadcopter. Make sure to watch it full screen. Enjoy!