How can I export 1920X1080 to 320X240 without losing quality?
No matter what you try, you will lose quality as you are reducing the resolution significantly. So you are creating each new pixel from an aggregate of 36 - and depending on how you do that it can look okay or terrible, but it will not look anywhere near as good as the original. There is no way to avoid this.

Experiment with the settings for down sizing - for your video some may work better than others.