Yes, it is too early. The American Academy of Pediatrics and the World Health Organization (and others!) say you should exclusively breastfeed for 6 months before introducing solids. You can make enough milk for her if you feed her on demand. It is considered a myth that giving solids now will make her sleep through the night, though lots of moms will tell you that it did help their little ones.
It is very normal for breastfed babies to need to eat through the night at this age. It's actually NOT that typical for them to sleep through the night. At 4 months old they are starting to notice the world around them, and get more distracted when they eat (have you noticed this? LOL). They tend to take in less during the day, and have to make up for it at night. It's VERY normal. Plus, you may just now be experiencing the "3 month" growth spurt.
All in all, I would say do not give her cereal. It's not very nutritious and your baby is much better off just on your breastmilk. You can make enough as long as you feed her when she asks to be fed. It's the law of supply and demand, she is now demanding more which means you need to supply more. Your body will understand to make more if you put her to the breast more often.
I exclusively breastfed (and by that I mean breastmilk only, no solids whatsoever) my first for 7 months, the second for 8 months. My son was 20 lbs at 6 months old, but I knew my breastmilk was perfect for him. My daughter was more petite, but still very healthy and had a consistent growth curve. My baby is now 6 months old, still just breastmilk, and he's 19 lbs (he was a little smaller than big brother at birth), completely sustained on breastmilk. This isn't necessarily because I've got super milk (though, really....don't we all?! I think it is miraculous that our bodies feed our babies!). I think it's because I've always fed the babies on demand.
It's also very important to remember the guidelines for when baby is ready. I see people who put their babies in reclining high chairs in order to feed their babies who can't sit up yet - this is too early. Developmental signs of readiness are:
Baby can sit up well without support.
Baby has lost the tongue-thrust reflex and does not automatically push solids out of his mouth with his tongue.
Baby is ready and willing to chew.
Baby is developing a “pincer” grasp, where he picks up food or other objects between thumb and forefinger. Using the fingers and scraping the food into the palm of the hand (palmar grasp) does not substitute for pincer grasp development.
Baby is eager to participate in mealtime and may try to grab food and put it in his mouth.
All of these should be in place before considering solids. This is a great place to read about starting solids when breastfeeding: http://www.kellymom.com/nutrition/solids/solids-when.html
Parents can make the choice, but I think people are too eager to give solids. It's not recommended by the major health organizations, yet pediatricians and mothers all seem to think it's okay at 4 months. Your baby most likely is NOT ready.
***ETA I've read other posts and everyone has a right to their opinion. However, delaying solids until 6 months is definitely NOT hogwash: it is what is recommended by ALL the mahor health organizations of the world. How is that hogwash? It's not just about allergies: it's also about whether or not baby's digestive system is mature and the real experts in this area (and by that I do NOT mean Gerber industries, nor pediatricians) agree that babies do not have a mature enough digestive system until then.