My best advice is to contact your local county agriculture agent and ask him/her this question. Their advice is free. Your tax dollars pay their salaries, etc., so take advantage of their expertise.
I would incline to transplant the tree in the spring so that new root growth would help the tree to get rooted in its new space, and so that it would have a chance to recover before hot weather arrives, assuming you ever get that. Here in North Texas we will have temps in the low hundreds (100-108º F.) within the next few days and transplanting a tree of any size in those temperatures would likely kill it.
Make sure to give the tree plenty of water when you transplant it and for several weeks after. Also make sure the place you transplant it to will have good drainage and not be too close to buildings, driveways, sidewalks, etc., because at some point the tree's roots may be a problem for these things, causing them to rupture and crack or break up.