Formula won't make your baby sleep longer, she is 3 months old and will hit the biggest growth spurt any time now, and she'll want to eat constantly, so just nurse her when she is hungry.
I agree with the others, I don't get why doctors pus hformula. I know they get a big kickback from formula companies (which should be illegal anyway) but c'mon, if your baby is nursing good, then let the relationship be.
Formula is harder to digest, her little body will have to work twice as hard to digest it. I do'nt think thats a better route at all. Breastmilk has EVERYTHING she needs, its tailor made for HER and changes every feeding to meet her needs! Formula cannot do that, ever. Plus breastmilk is alive, it has antibodies in it that protect her, line her belly, its easy to digest, and has a way higher fat content than formula.
If she is nursing good, then let her nurse. ITs not worth it by using formula.