I quilt my own. I have had 2 quilted by others, but simply can't afford it. Yes, you CAN handle at least a large queen on a domestic. However, with moving such a heavy fabric sandwich, limit yourself to about an hour a day (or twice a day for an hour). Otherwise, you get exhausted, irritated and make mistakes.
I recently bought a Bernina 440 QE. If you can afford it in future, save for a quilter's machine. They usually have 2-3 more inches between the needle and motor housing and this makes a HUGE difference!