Quicktime Conversion not available?

When I try to convert a video from a .mov to a .avi, I can't do it. I go to File>Export, but it doesn't show "Conversion" anywhere. All it shows is the different settings such as "1080p, 720p, and 480p," as a few examples.

While the AVI file container is still playback supported under Mavericks, Yosemite, and El Capitan, QT X based apps do not have the capability to export AVI file content. These apps only export to default compression formats like H.264/AAC (distribution) and ProRes422/PCM (editing) targeted content. Thus, the current export options only target device resolutions which, in turn, determine the context adaptive encode settings. If you MUST convert your video content to AVI, then you will need to provide additional information regarding end use and/or codec requirements which will then determine what app or workflow may best suit to your individual needs. For instance, if the AVI files have to also be compatible with QT X playback, you'd need an app that will create properly encoded MJPEG/LPCM AVI files. On the other hand, many third-party converters will likely produce common AVI distribution files in the DivX/MP3 format. Still other workflows can create DV AVI files that are required/preferred by some third-party video editing apps.

I also want to convert the file to a smaller size. It is a 2.1 gigabyte file, even though it's only 1 minute 45 seconds. Is there any way to convert it smaller?

Any conversion having a lower combined AV data rate than your source file will be smaller. In this case, more efficient codecs with produce the smallest files while retaining the most quality.