I don't practise in immigration law, but have some general AAT experience. You can generally appeal to the Federal Court from the AAT on a question of law - but not on a question of fact.
In other words, and put over simply for example purposes, if the AAT determined that today is Wednesday and the law says you can't enter the country on a Wednesday:
- you could not appeal to the Federal Court to ask them to determine it was not Wednesday; but
- you could appeal to the Federal Court on the basis that the law does not prohibit entry on a Wednesday.