Yes: one Export option is Movie to Picture, and this will take the current frame and export it as a PICT. PICT is a QuickDraw container, and it supports storing the image with various codecs; but it's primarily a Mac format. So you could take that PICT and put it in a document or slide show on a Mac, but it's not a file you could universally share with someone that uses Windows or Linux. (I don't know if it will sync with an iPod....)
Another option with QuickTime Player Pro is to copy that single frame, and then create a new movie with that frame; then Export using Movie to Image Sequence. Here, it will create regular bitmap files, and since it's a single-frame movie, you will get one file that you can easily share.
It's probably easier to get MPEG Streamclip, which has a separate Export Frame menu item.