It should be an acceptable answer, unless British English is more strict in the usage.
If we were beside a lake, I could easily ask 'are you going in the water'. So surely that should be an acceptable translation?
"Are you going in the water" should be accepted. Of course "in" in German means "into", but when speaking of water, what's the difference? You cannot go "in" water in any other way without going "into". Duo is splitting hairs on a bald man; there is no "there" there. Which is why British and American English would use "in" and "into" interchangeably in this context.
"Are you going in the water" has to be accepted here. I understand the distinction that Duo is trying to draw, but an American would very rarely say it that way.
If I ask anyone if he or she is going into the water, it is the same question as Are you getting wet? Isn't it?
No. Someone can get wet by standing in the rain, for example; that's not "going into the water".
And if they have a drysuit on, they might even go into the water without getting wet.