There is a good chance that the 1.2A is an excessive rating, given the large difference between the 3.0A rating on the QC and the actual current draw. But you really need to test it to be sure. I started looking into this because I had a VooDoo Lab Pedal Power 3+ that has 2.0A of pass through power and VooDoo Lab states that you can run a QC off of it. But I wanted to be sure so I patched an old daisy chain cable between the QC and the power cord, sliced open the sheathing, and clipped in my multimeter to measure the draw of the QC. There is a whole posting string about it. Here is the specific post where I detail the QC power requirements:
If you want to do it, I followed what another guy did in this YT video and it worked just fine. You do need a spare daisy chain power cable that you don’t mind butchering a little.