I've tried to do it using my gmail account, but when I email my @ugrad address the email doesn't get forwarded and when I email my @student address it does forward to my gmail, but with an attached error message, and it doesn't appear in my uni email (even though I've selected the option to save a copy).. 
Not sure what you mean here with @ugrad and @student addresses. Are we supposed to have more than one university address? The welcome email in the inbox seemed to only indicate having an @ugrad.unimelb.edu.au address.
I have a filter set up (Portal -> Email Tab -> Options -> Message Filters -> Add A New Rule) that looks like this:
"For ALL incoming messages; redirect it to the email address
[email protected]. Also keep a local copy."
So far all email I've had to my university address has properly forwarded to my Gmail, and also remained in the university webmail inbox so I can access it from the portal. Seems to be working fine for me.
Additionally, in my Gmail settings I have set up my @ugrad.unimelb.edu.au as one of my addresses (Mail Options -> Accounts and Import -> Send Mail As), so I can send email from my university address straight from Gmail, bypassing the portal entirely, which seems useful given that they seem to want students to use it for university correspondence despite the webmail being rather inconvenient.
If it's a matter of the forwarded email not showing up in your Gmail inbox, it could be because Gmail tends to be a bit retarded about displaying emails "from" the same address (it doesn't), so if you're trying to test it by sending an email Gmail -> Unimelb -> Gmail all from the same Gmail account, the "from" address is probably the same so it doesn't like it. If that's the case, try having a friend send something to test the forwarding settings instead.