You need to keep it supported with stakes. Once it is stable it will start to grow more roots. I would also suggest mounding up some soil around the crown or base, this will stimulate more adventitious root growth. if you get some heavy duty stakes it should start growing roots by summer when it heats up.

good luck

It will definitely establish its roots once it starts rooting. I had this problem with my bottle palm and I added some more dirt and got a stake to keep it up and after about a month of summer weather it was study again.
As long as its healthy, it should have no problem getting some solid roots.
Good luck!
-Alex

I'm no expert by a long shot, but from the photo, your soil looks to be really dry and hard. Can it even root in that soil? Maybe you could remove the tree and prepare a nice, big planting hole with better soil.....something a little richer and moister and softer. Then replant, stake it for a while and see what happens.

Thanks for all your advice. I'll add 4 large stakes for support.

bill: the soil is not the best, but not that hard, it gets hot and dry here in my area in the summer, and wet and cold in the winter. However, I have 2 other Queen palms that are growing fine.