I would say that it's not a good idea to try a Disk Utility repair of a system that is newer than the version of Disk Utility.
Here's a method that you can always use (and does not need to boot to another disk at all)
Boot into single-user mode: restart, while holding Command-S
You'll get a screen with text scrolling down. It will stop at a prompt.
At that prompt, type: fsck -fy
then press enter. You'll see several lines showing that various disk tests are running.
If that test ends in some kind of error, run that same fsck -fy again, until no problems are found.
If you get the same errors, and continue to get the same errors 2 more times, then you would need to run a more capable disk repair.
I recommend Disk Warrior.
That being said - why do you need to run a disk repair? What problems are you experiencing now?
Thanks DeltaMac. Startup disk is almost full. (I got it down from "is full" by deleting the Japanese dictionaries.) I ran verify disk and it told me to run repair. Can I burn the installer disk from this machine using a download?