Happier? No. I don't get the impression happier is a goal of the Qun. You see, the Qun doesn't care about individuals in the slightest. The Qun is set up to care only about the Qun as a whole. There is no happiness in the Qun.
I think this is where many people seem to disconnect. You assume that life in the Qun would be JUST like your life now, except everyone is "equal". That is NOT the case. They are a living breathing MACHINE society. They value efficiency and devotion to the Qun.... nothing else. There is no families, they wouldn't live in individual homes but barracks. They would have no 'possessions' of their own. Their 'friends' would only be those that they work close to each day. You would be working long hours each and every day with little to no rest time. You would always be under the watchful eyes of the secret police and you can't trust any other Qunari should you start to think dissenting thoughts, as ANY of them would turn you in instantly should they know.
If should become injured or sick, sure they might have the best medical treatments around, but if its something they can't fix and your ever unlikely to be able to return to a productive life... they would kill you. They care nothing for the individual, only your worth to society.
Individuals are nothing more than cells in the Qunari body, and a body spends no thought or compassion on cells dying if that benefits the whole. Right now in your body there are cells on 'patrol' looking for cells that no longer perform their function and eradicate them.
Qunari values are not anything like the values that the vast majority of people hold dear. I would be willing to bet that 90% of converts to the Qun eventually go through the re-education process (ie mind-wiping) simply because they found the Qun to be wholly different from the idealistic vision that it paints for itself.