Couple of things you can do. Either download the VCL player which is free and will play any format of media file. If you still insist on using Quicktime, then you could use Handbrake (again a free download) to convert to a format usable by Quicktime. I do this so I can play movie files through Itunes and on my Ipod.
I'm fairly sure that Quicktime doesn't play avi files.
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