Yeah you have to buffer your skills, just not that much. I used to QWR all the time. Now, I try to QR, get 2-3 AA then W, 2-3 AA, rinse and repeat. Also, try not to use your E. Unless I am wrong, AND PLEASE CORRECT ME IF I AM, but if you use your E you lose the passive effect. In which case, I have not been using my E so as to have that passive on all the time.
Furthermore, the first item I build is Nashors, and I think that is objectively the first item you should build unless you are jungling. I also build the AS boots instead of magic pen because that extra AS means more mp thus more skill spam, and less wait time between skills since you get your 3 autos in quicker.
Also, keep in mind what I said that she is still very weak at low levels. lv 1 and 2 she still doesnt have her e passive, and pre 6 you dont have ult. I think diana becomes really deadly after you build nashors and the as boots. for my third item i either build gunblade or lich bane, unless i need some defense in which case I build banshees or zhonyas. Both of those items are great imo because one gives you LS which gives you more room to buffer your skills for AA, the other gives you CDR and stronger AA. 90% of the time my build is [Nashors, AS boots, gunblade, lich bane, zhonyas or banshees, rabadons].
Does that help? Give it a try and let me know if it helps.