I agree..lacy may not be what you want if it's for warmth.
That seems like a lot of stitches for a 3 mos old baby hat. What weight yarn did you use? For adults I usually use worsted weight and cast on 80 or so.
I should also point out that there are hundreds of hat patterns for various sizes. If it's just a basic hat in stockinette stitch we can direct you to hats in adult sizes.