If Denmark goes the way of Iceland, Denmark may condition this on there being at least 14 days after the vaccine regimen's second/final shot.
June 2nd shot to June 15th arrival seems like it could potentially pose a problem to meet the vaccination requirement. So it'll either be test requirement or no-go.
The Swedish infection scene for children is not pretty right now, so it's to be seen what Denmark decides to do about Swedish kids in the weeks and month ahead.