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.