I've already installed Ubuntu 12.04, but I did not make any separate partitions beside the one the operating system is installed on.
Now I want to make a new such partition.
Is this possible?
Open gparted via a Live CD
why live cd:
Gparted cannot modify mounted drives and since you only have 1 partition that means its the one running ubuntu. So you will have to open the live cd and do your edits from there.
What is a live CD:
If I understand (correct me if not) you installed Ubuntu to along all your 1TB HDD.