Interestingly, several people are reporting that they're able to copy characters over successfully.
This is rather surprising, because despite the recent class changes many of us weren't expecting the PTR until next week at the earliest. Perhaps this is a sign that it'll come earlier, or at least is in the "getting ready" stage for public release.
This PTR is going to be huge, on the scale of patch 2.4 when they released the Sunwell.
We'll have more up on WoW Insider the second we hear it, and don't forget to check out our coverage of Patch 3.1.
Update 12:45 p.m. EST: We're getting several reports that US/NA people can copy over characters to the US PTR now.