She's like a strange mix of Akali and Vi, but yeah Vi can dash twice in one rotation, and so can Diana. Diana's power spike is a lvl 6, where she can burst down a squishy pretty quickly once she gets her ult even without items. And yes, most people build her to be pretty tanky because usually once she goes into a team, she has no way to go out of it unless you can ninja your way out with a Q > R into a jungle camp or minions or something. In a nutshell, she's a somewhat tanky assassin.
While she might be a bit difficult to grasp at first because of her Q being a curved skillshot that takes some time getting used to, her general combo is pretty easy once you get the hang of it: Q > R > AA > W > AA > E > AA > R. AA meaning autoattacks; mix in auto attacks for maximum effect because of her passive. If you have Q up again before the second R, slap them with it before ulting in so that you can get it to remain refreshed shall you need it again.
Oh, and the new protobelt item was just MADE for her. It adds more to her burst, a bit more mobility, and some tankiness. Plus, if you follow E up with a protobelt blast, most of the rockets are going to hit the target, softening them up if not killing them.