When you copy from one share to another the data is copied through the network, so it has to be transferred twice. AFAIK the NS1 doesn't have a vendor supplied way to copy data directly between two shares, except the backup function which copies between internal and external disk.
However, it is possbile to
get shell access, and do the copy action on the NAS itself. It is also possible to change the provided html file a little to do a webinterface backup action from one share to another, no matter if they are on in- or external disk. You should still not expect high transferrates (the NS1 is a rather limited device), but at least you can switch off your laptop during copying.