It should be okay. I transplanted some last fall and they did fine.

They'll be just fine. Its hard to kill raspberries...trust me..i've tried. I actually have about a dozen in pots that need to go in the ground once this heat lets up.

Fall transplant season here in Wisconsin might run from September 15 to October 15. The idea is to plant late enough that the shorter days and longer nights give the plant some relief from sunlight, and yet, allow some time for the roots to develop and grow a bit before winter sets in, and the ground freezes. I have successfully transplanted blueberry shrubs in the fall, and it is commonly done with all sorts of trees. It should work with raspberry canes, as well, I would think.

Awesome, thanks for the encouragement!

Yes fall is the very best time to do it. i would not do it in the spring. You would probably lose the season, they would survive, but you would lose the season, or some or most of it. Doing it now you should get a full season next year.