My /home dir has only about 5GB left so I got a new hard drive.
Now after creating some partitions in it, I want to use one of them as home and use the previous home for some other purpose.

This is what I think I should do:
1) Copy all the data from the old home to the new home.
2) Change the old home in fstab and passwd files.

Is this method feasible or do I need to do something more/less so my current system doesn't break?

ok heres a brief summary

1 - backup everything (just in case)
2 - setup new disk (e.g logical volumes or however you wish to do it)
3 - login in as root
4 - mount the new disk to a temporary location
5 -copy /home to new mount point
6- umount temporary mount point and /home
7 - edit /etc/fstab to mount the new disk into /home
8 - mount /home
9 - login as normal user and test all is ok.
10 - Fetch beer and admire handy work !!

If anything goes wrong you have from 1 a backup (you didn't skip this did you ?) and also if you just copied the old /home you should still be able to mount that as well.