Oh, sure they do! WiebeTech has a number of SATA -> FireWire bridges, using the Oxford chipset. Take a look at
http://www.wiebetech.com, and you'll find something to your liking.
Once you've made the backup to that drive, what you'll do is boot the new Mac mini and use its built-in Migration Assistant (which appears during the first boot) to migrate your files from the backup to the new mini. That'll retain the new iLife and bring in your other 3rd party apps, files, etc. It'll work great.
Hope that helps.