It's definitely tension related. Your stitching is beautiful, so once you have the tension figured out, I think you'll love the FMQ.
Assuming that your tension setting is 0 - 9 for the needle thread tension, 9 is extremely tight. You should be breaking the top thread instead of having eyelashes on the bottom. If it's to 30 or something, then it's probably not enough needle thread tension.
I had to look a second time at the photos, but I don't think your upper threading is right (again, assuming that 9 is the tightest setting on your tension dial)
In your photo, you have the occasional loose thread on the top as well. There's a lot of thread being pulled through without enough regulation. I think that your tension disks aren't holding the thread enough. Either there's fluff holding them apart, hence your need to crank up the tension setting, or the thread is just laying in the tensioner, not right in between the disks.
ETA: or as others have mentioned, the presser foot is up, and you're effectively sewing with 0 tension.
Clean your tension disks on the top (a little dental floss helps) , make sure the bobbin thread is leaving the case in the correct direction, drop your thread tension to about midway and rethread the machine.
When I thread, I do it in a weird way (which breaks the "rule" of threading always with your presser foot up) but I don't have issues with the tension disks not having a good grip on the thread.
1. Thread the machine with the presser foot up until you've threaded through the tension disks
2. Drop the presser foot
3. Grab both sides of thread as it enters and leaves the tension disks
4. give a gentle tug so that they're fully seated into the tension disks (if the thensioner is one of the "exposed" ones like on the older machines, and the thread makes a "V" going in and coming out of the tensioner, you can tell by how close the threads are to each other if they're fully seated)
5. Raise the presser foot, and continue threading the rest of the machine.
With my very limited experience with FMQ, I find I tend to have to lower my needle thread tension a smidge from regular sewing on some machines, but if you lower at this point without finding the actual source of the problem, you'll end up with nests.
ETA: What machine are you using to do this? If I can see a photo of it, I can help with the tension settings.
Additionally, here's a test you can try to figure out which thread tension is giving you fits:
http://www.quiltingboard.com/vintage...ml#post5941686