No, it's more positive than that. It means a happy, positive personality. 'Irresponsible' is closer to 'careless'. I hope this helps. :D

"Cares" can mean "worries." They are things you need to "take care of." It's common to observe that heads of state "age in office," start to look old and worried--"careworn." A "carefree" person is simply one who is free from cares--free from duties, free from worries.

A carefree person is someone without any worries. It doesn't mean that they are irresponsible, just that they don't have anything to worry about.