You can compare systems at everymac.com, the geekbench ratings give a fair idea of what render times will be, but other aspects of editing are affected by things like the graphics chip, disk speed, etc. They don't have geekbench ratings for the new MBA yet, but it is only slightly faster than the 2015 1.6ghz model (BTW, your new MBA is actually considered a 2015 model, since nothing changed in the design but 0.2 mhz cpu upgrade).
You 2012 MBP and the original 2015 1.6ghz MBA have the same geekbench rating - about 5700, so your 1.8ghz MBA is going to be slightly faster, probably not enough to be noticeable.
http://www.everymac.com/systems/app...re-i5-2.5-13-mid-2012-unibody-usb3-specs.html
http://www.everymac.com/systems/app...book-air-core-i5-1.6-13-early-2015-specs.html
But the MBA has a graphics card 2 generations newer than your MBP. Probably the most significant difference there is that your MBP only supports 768MB of video RAM which is very limited while the MBA supports twice as much (1.5gb) but still not a lot by today's standards. Some high end software will not run on either machine for example.
The main limitation of the MBA for video editing IMO is the lack of ports for peripherals. I use thunderbolt for a blackmagic ultrastudio interface that drives a Sony production monitor. FCP sees this as an "external video device" and it sends full quality video to it so you can see what the finished video will look like. Without this, you are limited to a lower quality display while you edit. Some Macs support external video via HDMI, but the MBA doesn't so you need some kind of box like the ultrastudio to do the "heavy lifting".
Anyway, since this uses the thunderbolt port, you need to have the FCP timeline, browsers, etc on the little MBA screen which is rather limiting. I'm working with a lot of legacy video and need a firewire port to connect a pro video deck and again the MBA doesn't offer that. One solution is to get a thunderbolt dock. Tried that and it wouldn't work properly so I ended up getting the mini and use it as a dedicated video editing machine.
Anyway, for the light usage you describe, I think the MBA will be fine. If your son gets more serious about video then you can look for a more powerful machine at that time. Having been there myself, I don't think it makes sense spend much money to "upgrade" the MBA for video since it will always have some limits like the graphics chip and 8gb max RAM.