The QM2 was built to cross the atlantic so can tackle the worst of weather may and june should be a good time to cross.
We sailed transatlantic on qm2 at the end of may 2006. The weather was windy but sunny and we never had any problems. The ship was steady and smooth and you really wouldn't know you were on the ocean till you looked out of the window. Access to the highest decks was restricted because of the wind but that was the only slight inconveniece. The trip was a fantastic experience and I am completely spoilt now and can't begin to comtemplate travelling on any other ship; apart from queen victoria when she launches. If you are considering going or have booked you will have a wonderful journey.