Luke was a moisture farmer raised in relative comfort by his aunt and uncle. Rey grew up fending for herself as a scavenger, fighting every day to stay alive, learning the skills and abilities she need to along the way.
Luke was a naive, cocky kid going out on his own for the first time in Star Wars. Rey has been on her own most of her life. She can handle herself because if she couldn't, she'd be dead.
As an aside, Luke blocked a laser blast while blind on his first training session. Without further training he disabled his targeting computer and fired from sight/touch a pinpoint shot at the end of the film, guided by the force. Daisy was put in situations where 1) she was seeing what a force user was capable of, and 2) testing herself 3) because if she didn't she was dead. Luke wasn't really put in those situations until after he'd had at least some training. (I think it's also implied that she's a more naturally gifted force user.)
Her arc is fine.