No, the two letters have different sounds.
http://forvo.com/search/skj%C3%B8rt%20skjorte/ http://www.skapago.eu/nils/en/resources/pronunciation https://www.duolingo.com/comment/13524612 (Check this one out in a seperate window so you don't lose your place in this lesson.)
So "skjørt" which sounds (to me) closer to "shirt" means "skirt" and "skjorte" which means "shirt" sounds to me like "shortah"., but I am American and to Norwegians the ø is a very specific sound which is different from anything that we have.
I got tested on the audio transcription, is there any reason it couldn't have been "ett kort skjørt"? In the numbers lesson, it says:
Keep in mind this distinction only exists in writing, because the words above sound just like the indefinite articles. In spoken Norwegian, only a verbal stress on the article can signify one.
I tried to report it, but there was no option for "my answer should have been correct". Perhaps the team is already aware of this?