I agree with Dude and others, focus more on reading to her and let her lead you to the amount/level of reading she wants to do on her own. You could also encourage her to jump in when you are reading if she sees a word she knows/wants to try to read. Sometimes I ask, do you see any words you know on this page? And then after DS would tell me which ones, I would let him read those words and I would read the rest. Sometimes I would challenge him if there was a word he didn't point out that I know he knew or could figure out. Sometimes he would take the bait, sometimes not. If he didn't I just read that word too. He also really liked to repeat after me, which I always thought was a little weird but have since learned is a common learning to read strategy.
My goal has always been to make reading fun. I want my kids to be life-long readers and to discover the joy of reading. Especially at 3, I would really recommend emphasizing book enjoyment over performance.
Also, I am not sure I would attach the fine motor skill challenge of peeling the star off herself, to the reward you are trying to hand out. It seems like rewarding the achievement of a difficult task with another difficult task might not be the best approach. In fact, I would not really "reward" the reading because to me it should be a reward in itself. Praise from you for sticking with it and not giving up should be sufficient. And again, if it isn't fun for her, I would recommend choosing a different approach.
And, strangely the sounding out of words can take time to figure out even when the child knows all of the sounds individually. Something about putting them together can be tricky. Then all of a sudden it clicks and they jump forward! But the time frame from each learning point to the next is very individual.
