Currants, red or black, root incredibly easily. You can shove pieces in the ground any time and they will almost certainly root. If you do it now where you want the hedge I would expect them to be rooted by the Autumn. I moved my black currants three feet by simple sticking pieces in the earth three feet from the old row. Do not keep them inside in the winter. They need a dormant season, not to be forced to grow all winter.

In your climate, if you are going to start cuttings as floral suggests, I would do it now. It is important that your cuttings grow enough before winter that they can withstand the winter, no problem in my zone. Al