Of course! IIRC Vista should be able to create mirrors via software, that is directly from the disk manager and w/o needing a dedicated hardware raid controller. If I am wrong, you will simply not find some of the menu items I am listing below.
I am basing the simple procedure below on Windows 7, but Vista should be pretty much the same in terms of menu structure.

0. Connect the new drive to your PC. Possibly placing it in its final location and using its final SATA port and cable. So you won't have to remove it later. It'll just stay there "for good". Boot your PC.
1. Start->Right-click on "my computer"->Manage
2. Storage->Disk Management.
3. Activate/import (whatever needed) your new disk, and upgrade it to Dynamic
4. Upgrade your old disk to Dynamic if it is still basic (right-click where it says basic)
5. Right-click to your old disk, selec "Create Mirror" . If Vista has this feature locked for license reasons (As I was saying, I can't remember which of Vista flavours, other than the Server - aka Windows Server 2008 R1 - is capable of doing mirrors and which is not) you will simpli not find the option there and this whole thing is not possible.
If you find the "create mirror" option, just click on it and select the new disk when prompted.
6. Let it build the mirror. It may take from 10 minutes to hrs, depending on the size of your disks, more precisely on the amd of data in the old disk. In your case, I'd expect 20 mins.
7. When done, you have a mirror system in place. Reboot your machine, just to be sure all is ok.
8. Shut down, remove old disk from your case, boot again. You will be prompted whether you want to boot from the mirror (C: duplex) disk as the old one is gone. Say yes. You system will boot, and if all is ok it will be blazing fast due to the SSD.
8. Logon, back to the Disk Manager. You will find your old disk there, marked as missing. Right-click on it, select to break mirror, accept all disclaimers, and then "remove" it logically (right click, remove).
9. Done.

Should anything go wrong, you can always plug your old disk in and boot from there, so it is fairly safe.

I've done this zillions of times in Windows Server of all flavors in the last 10 years, since Windows Server 2000 times, and I never had an issue. And, you've got 9 points up here just because I am trying to giude you step by step. What you're doing is really a piece of cake process, quite obvious and streight-forward.

I actually keep a mirror in my home server as well, so my HDD upgrades simply involve adding a couple of steps to create a new, larger mirror. Very convenient and simple.

I hope this helps. If not, let me know and I'll try better



Edit:
I forgot. When the process is complete, you will find yourself with a 80GB partition only in the new 128GB SSD. Still in disk manager, right click on the partition and expand it to fill the remaining space. Remember its a "Dynamic" disk, you can do a lot more basic formatting, resizing, moving stuff with it, now.