How to move files via SSH from Hostgator to Godaddy directly? Possible?

How to move files via SSH from Hostgator to Godaddy directly? Possible?

It's my first time using SSH and so far I managed to connect via SSH to my
Hostgator server. What I aim to do is to move files from my Hostgator
account, to my Godaddy hosting account and file size is about 1Gb so FTP
is out of the question since it would take forever (I tried earlier with
FTP).
Now I'm trying to setup a SSH tunnel directly between my Hostgator and
Godaddy so I can transfer files directly and much faster, but I'm stuck in
this part.
Should I open two SSH sessions? Could you experienced geeks help move me
in the right direction? I did research for a few hours and I still feel
like I'm lost in this part.