Queen Palm Seedlings All Over The Ground

This happens every year. The queen palms drop thousands of bright orange fruit. The fruit dries out on the ground, and then all those seeds begin to germinate. I wish it was closer to Christmas...I'd give them away as presents. They really are pretty cute.

Here's the first one from this year's drop. It found its way under the peach tree and germinated because it was on sandy soil, gets regaulr drip irrigation misting, and because it gets lots of filtered light. Now, I have a few buddies in Ft. Pierce that will know what I'm supposed to do next. I'd like to rear these young pups. What do I do now? Can I move it? Do I plant it in sandy soil? How deep?