I have quilted a full sized quilt on my domestic machine and the experiance...well, lets say there was a lot of swearing involved. Didn't help that it was a denim top and that made it heavy and even harder to work on. And it was just a simple top just made with 4" squares and I stitched an X in every other one...and that was HARD! I can't imagine quilting a queen sized top. I'd take it in to the long arm quilter, espessily since its a queen as well as your first top. Might cost you a little money, but you'll save on sanity. ;)
Not to say you can't try quilting smaller things like table runners, wall hangings, or baby quilts.