I have a 2013 MacBook Air with 8 GB of RAM and it can edit 1080p HD video like a champ. Current generation MacBook Air should be able to handle full HD video editing just as well. Not sure if it can handle 4K video though.
I had a 2011 i5/4gb/256gb MBA and upgraded to a 2013 i7/8gb/512gb MBA. Don't know anything about GoPro, but I edit Sony XDCAM-EX 1080/24p HD video and the 2011 machine handled that fine. The 2013 renders faster but otherwise is pretty similar.
The 2011 MBA does not have USB 3.0 so that is one big limitation however. The SD memory card slot on the 13" 2011 MBA is also connected to the USB 2.0 bus and is much slower than newer models. And the SSD is much slower on the 2011 MBA, which impacts performance.