felkel has more an idea of getting out of bed. Kel could just mean to get vertical.
"To wake up" is "felébredni". That is when you stop being asleep.
"To get up" is "felkelni". When you get out of bed.
It sounds a bit weird to me like that, with the prefix attached, but you can try moving it a little to the back: "Szeretsz korán kelni fel?" There's not much difference in meaning between this and the given translation.