Depending on how you perform the copy of the data, if you are using your laptop and Windows Explorer to copy the data from one NAS to the next, perhaps copying the data from one network drive to another, then I believe the data copy does go through your laptop since that is the device working as the device in the middle. You could however perform a direct copy of the data from one NAS to the next. As another user mentioned most NAS devices can use FTP, however if you have the option to use RSYNC, then I would go with that method.
Many NAS devices have some version of Linux running in them and as such they probably can perform an RSYNC directly between the two, thus eliminating your laptop as the bottleneck and you might be able to do a block level backup which will only back the data in the file that has changed instead of the whole file, which will lessen the demands on the network.
Another thing you can do to improve the performance between the two NAS devices is to place both of them on the same switch and if you can Link aggregate the NICs on the NAS devices then that too will help, and better yet if you can have a dedicated switch for the NAS devices to connect to, then have the "NAS switch" connected to the LAN, it will also help reduce the additional traffic that would be on the network between the two NAS's
I hope this was helpful, good luck