There has been no date given for it at all. Since it would make sense to do this once the population of the server with the least players gets too low, you might be waiting a while...
So you are probably best of just re-rolling on the server you want to be on. Note that you can transfer AD between servers (by buying ZEN on one and withdrawing it on a character on another server).
Create a new character on their server. It takes a week or less to get to 60 and if you invoke and do some leadership the toonling will have enough AD for tier one and perhaps tier 2 by then.
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So you are probably best of just re-rolling on the server you want to be on. Note that you can transfer AD between servers (by buying ZEN on one and withdrawing it on a character on another server).