USA is one of the exception countries in the world, where mamas are rushing to give their babies some solid foods, including cereals ... to either get their babies to sleep longer at night, or to grow their bodies faster than nature intended.
Please DO NOT GIVE ANY CEREAL TO A BABY LESS THAN 6 MONTHS OLD. It is best if you can wait till she is 8 months old.
Her digestive system, particularly her intestines, are not mature enough to bear the load of a cereal. At 4 months of age, your baby girl has an "open gut" ... her small intestines are not fully covered with a protective lining ... not till she is at least 6 months old.
So, when you feed cereal to her, allergens or proteins leak from her intestines directly into her bloodstream. This is harmful in a variety of ways (allergies, respiratory illness, future obesity, health problems in later age) ... ask your pediatrician or look up the internet.
Moreover, a cereal feeding forces the baby's body to focus on digesting the cereal (which is an overload on her body), instead of spending all energies on maturing her digestive tract.
There should be no hurry. Please wait till she is at least 6 months old, to feed her any kind of solids. Enjoy her.