Is Mountain Lion automatically protected against this malware?

If the computer had that, it will be moved to the computer. http://support.apple.com/kb/DL1517

Install the application and it deletes the virus

Technically, getting rid of Flashback (if you actually have it) is a little more complicated. The Flashback removal update that mende1 recommended is only applicable to people who are running Lion and do not have Java installed. If you do have Java installed, there is a different update that you will need. And these updates cannot be installed more than once... if you have already installed either, you should be Flashback-free, with security tightened down to prevent future infections (of which there probably won't be any, as Flashback hasn't infected any new machines in months).

For more information, see About the Flashback malware.

I think the OP may have a point here. It sounds like there wasn't a very big gap between his old an new computer, but say it was six months or so, before most users had even heard of Flashback. He could have migrated components of it very easily since most were contained in his user directory.

I had a discussion with a similar user a few days ago and he went to the trouble of running all the Flashback and MacDefender removal tools (that he had saved) on his new Mountain Lion Mac and they all seemed to run. I don't know enough about the directory structure of Mountain Lion to know whether any of them would have been effective or not, so I think there could be a very slim chance that an infection can be migrated. The XProtect system only looks for installers and GateKeeper watches Applications. It would appear that the MRT's look for installed components as do many third party general A-V apps and Flashback removal tools.

I think I missed the fact that the data was restored to a ML system, which does complicate things. Those third-party tools should all work just fine in Mountain Lion, at least as far as the directory structure goes. Not that much has changed. But the Apple-provided updates definitely wouldn't work, as they're for Lion and shouldn't even install on Mountain Lion.