Well, that was my concern. I don't think they share GND. Did I screw something up in my schematic?
You've used the same ground symbol, which implies they're connected together. Myself and many others assumed they were separate grounds, because of the question, but some people took the schematic more literally.
I have 2 windings on the secondary one for 12VAC and one for 6VAC. After rectification, smoothing and drop down, they are two rails with two distinct GNDs.
Can I common the GND between the two different rails?
Yes, in this case, you can connect the grounds and just use the MOSFET. Sometimes this isn't desirable. For example, if the fan was in a car, connected to a 0V wire carrying a large current from other loads, then connecting the 0V wire to the 0V on a logic board, could cause a large current to flow through the thin 0V trace, resulting in overheating.
Also note that after rectification and smoothing, you'll get the peak mains AC voltage, minus a couple of diode drops, which will be 15.8V on the 12V side, but could be more, when it's unloaded.