Would it be messed up to date my ex-girlfriends sister?

I broke up with my girlfriend because she was a total tool and a opportunistic, selfish, spoiled overgrown child. Her younger sister is totally different though, she's like her sister deserved it and she knows how I feel and we talk a lot and she makes me happy. She's actually kind and considerate and fun to be around. Would it be wrong for me to date her after I just broke up with my girlfriend like an hour ago?