In a word: no
Your baby is bigger than most, and may be ready to eat cereal sooner, but you aren't doing her any favors by providing cereal before her stomach and intestines are ready to digest it. That's why pediatricians suggest you start cereal at 6 months. I started mine at 5.5 months and it worked okay. (Mine ran about 9 pounds at birth) But as 12 weeks, I would simply provide a larger amount of formula at feeding time
I a assuming since you know how many ounces she ingests that you are bottle feeding. why don't you mix up a full bottle, feed her some, burp her, and then feed her more. Putting her fist in her mouth is not necessarily a sign of hunger. It's something to play with. It's something to DO that a baby can do. babies like to suck and fists are convenient sucking toys.
With a first baby, we all seem to want them to grow up and go through their stages quickly. If we could have a baby that grows up before we have our first babies, we would be more apt to relish the early days and enjoy each stage for what it is rather than want to rush through it. Getting to the point of feeding REAL food is fun, but it's fun when the baby's stomach is ready. Your pediatrician knows best. And I think the idea of starting at 4 months was a concession to your insistance that she eat more than milk.
I've had 4 kids, and as an aging parent, I would highly recommend you slow down and smell the roses along the way. We're talking 6 months at most, probably 5, of your life. Relax, take time to enjoy each day, because soon your baby will be away at school all day, and then she'll be a teen, and she may not want hugs and cuddles anymore. She'll be ready to let go of the apron strings long before you are. So relax and enjoy the warmth and the confinement of being so in demand. you will never get these days back again. (some of that is GOOD, too, but when your arms are empty, you'll remember those days and grin, wishing you could relive them -- not for months at at time, mind you, but for a day or so) It's impossible to understand this emotionally until your child is grown. You know it intellectually, but it doesn't "feel" like it will happen and you can't imagine the differences and how your life will change until it's done.
My advice? Set a life long pattern in place now, of trying to enjoy the reality of the life your child is living today, what her needs are, what new things she can do, etc. It sounds like you are doing some of that already. And work hard not to push your child to grow up too soon. Enjoy the sense of wonder a child brings to the world, and try to slow your own life down to accomodate that. You'll never regret it ! :-)