Yes...DiRT will work just fine in that scenario.
I wold recommend reading through the Cisco Unity Reconfiguration and Upgrade Guide:
http://www.cisco.com/en/US/products/sw/voicesw/ps2237/products_upgrade_guides_book09186a0080222fdf.html
Specifically the Replacing or Converting a Cisco Unity Server
Upgrade the current system to 4.2, run DiRT and then on the new system install the same version of Unity and restore, and you will be good to go.
It will save you some troubleshooting time when you set up the new Unity, if you make sure it works before you do the restore. You should be able to create some sample users and test that voicemail is working properly before you blow the database out and restore.
I did the same thing on our servers a little while ago and it went very well...just very time consuming.
Don't forget to get a new license file with the MAC address of the new server