Hi jodal,
you can do it in audition, but with no appropiate compression(i think) only uncompressed.
If you have your audo exported, open it with quick choose>export>qt movie>unchek video>check audio and export it to AAC for example. AAC gives good quality at low bitrates, For web-audience I would choose ~160kbit/s for purposes 320.
When the movie is exported open it with qt choose edit>mark all>copy- Open your rendered movie choose>edit>add to movie. If your movie contains already audio, choose window>movie proberties and uncheck or delete the old audio track.
When you just save your movie now, qt will link the audio to the original audio file/movie. If you want to save the audiostream within your original movie choose>file>save as standalone movie…
PS: I use a german qt version and translated all the dialogs badly. I’m sure they are named different in your version. But you should find your way easily.
Stefan