DO NOT give the baby cereal against your doctor's advice. Giving cereal sooner than their bodies are ready for it is never a good idea. There is an idea out there that the first three months of life is like a "fourth trimester" of sorts (Happiest Baby On The Block). We have to remember that these babies do not come out of the womb with ready-for-anything digestive systems. There's a reason why we're told to wait. And, there is no proof that giving cereal will help a baby sleep through the night. In fact, friends of mine that did it say their babies cried MORE at night, likely due tummy aches and the babies were constipated during that time. Once they stopped the cereal their crying at night was less and their bowl movements were more regular and softer.
Here's the thing.... Babies go through spurts of sleeping well and not sleeping well. And, yes, they do go through their first major spurt at about three months. Once your baby sleeps through the night, teething or a cold will come that will keep him up at night. Then that will be over and he'll be sleeping through for awhile. Then another growth spurt or more teeth or another cold, etc, and he'll wake up at night once in a while. Then as he gets older he'll be sleeping through, but then start to realize he can stall his way into going to bed, or cry at night to get you to come in and coddle him. I think parents just assume their child will sleep through after a few weeks of delivery and that's it. Not the case in most cases! Newborns are very sleepy most of the time...it's at around 3 mos old that they start coming out of that super-sleepiness stage.
I have a 3 year old and 20 month old daughters. We have been through times where they're sleeping great, then times when they're not for whatever reason - colds, teething, learning to stall, the holiday activity, etc etc. My suggestion is just learn to go with the flow, rule out any illnesses and try to keep the routine calm and consistant. Try to get the baby to have a big feed at the end of the night to hold him over, but otherwise, just chalk it up as absolutely normal.