Yes -- it can be done. It's relatively serious ubuntu systems administration so make sure you have a backup of anything you value and go carefully. You're going to research some techniques, learn a lot, sweat and cuss a bit and -- have fun!
In Windows, in VirtualBox, configure a new, bigger .vdi file for the ubuntu vdm.
Boot ubuntu and log on.
Open a terminal to get a command prompt.
From here on I'm assuming you're root. If you're not (that's the ubuntu way) then prefix all the command with sudo.
If you only have one disk already it's probably /dev/sda in which case the new disk will be /dev/sdb.
Assuming that's right, run cfdisk /dev/sda and note what partitions you already have. You will want to create similar (but some bigger!) on /dev/sdb.
Run cfdisk /dev/sdb. This should not show any partitions! Create the partition(s) you need. Type 83 Linux is a good choice and you'll want some swap.
Create file system(s) on you new partitions by mkfs.ext3 /dev/sdb<n> where <n> is 1, 2, 3 as required. Don't create a file system on the swap partition.
Now mount each partition in turn that has files you want to copy (all but swap) using mount /dev/sdb<n> /mnt and copy all the files from each old file system to the new. I never know the best way to do that so hopefully someone else will chip in. Maybe something like
cd <source directory>
tar c . | (cd /mnt; tar xp)
cp -dpR <source directory>var* <source directory>var.* /mnt
Shut down ubuntu.
Edit: after copying each file system, unmount it before going on to the next, using umount /mnt.
In Windows, in VirtualBox, de-configure the old .vdi file for the ubuntu vdm.
Boot ubuntu and, with a bit of luck and a fair wind, it's all set up as you want.