How to back up one mac to an external using another mac

I want to back up my old MacBook Pro onto an external hard drive. The old MacBook Pro is bad shape, hard to use in normal mode. The apple store genius told me I could use my new MacBook Air as a conduit for this back up. I purchased a FireWire cable with a Thunderbolt adapter for this purpose. I was attempting to use Migration Assistant to accomplish this back up, putting the old MacBook Pro in Target Disk mode, but from what I've read on these forums, mainly this article: Mac OS X v10.6: How to use Migration Assistant to transfer files from another Mac, it doesn't seem possible to back up onto an external given the options I am given in the process. So my question is (A) how do I back up one macbook in target disk mode onto an external using a second macbook as a conduit, and (B) is it possible to simply back up the old MacBook Pro while in Target Disk or Safe modes? Thanks so much for any help.