Not necessarily. Just like how not being a fighting seperates her physically from the others in our group, maybe not having problems will be what separates her mentally.
That said, our squad this time really dopesn't seem to have that many messed up people. Much more moderate than DA2 and even DAO in my opinion.
I wouldn't be so sure. We know for sure that Iron Bull has issues, Blackwall left the Wardens for a reason, Varric is probably suffering from Kirkwall, Sera is in a gang and has problems with people in power (that smells like traumatic backstory in 3, 2, 1...), Leliana has probably watched her friend Dorothea die and she can end up being tortured, Cullen collects Mage-Templar issues, Dorian is running away from his Tevinter family, and Cole... well, he is a walking issue.
That Josephine doesn't sound to have issues and has a background that seems to be acceptably issue-free is suspicious, but I would welcome the chance not to be a field psychologist with at least one character.