MANY babies, feed in this every 3 hours, or less, at this age. Its common.
She... probably hit a growth-spurt at 3 months (a typical growth-spurt age), and is still trying to make up for it by feeding more frequently in order to get in more intake.... and in light of the fact that she takes in only 3 ounces at a time. So, yes, she will feed more frequently. Each baby being different.
But, even big eating babies (like my son who had a ginormous appetite and drank like 6 ounces at this age & older), STILL FED EVERY 3 HOURS OR LESS... and "cluster=fed" at high growth/high development periods. This is also common.
And no, feeding her rice cereal will not stop the "problem" of her frequent feedings/wakings...and may also make it worse... or cause other problems or digestive problems. It is a myth, that feeding an infant cereal before 6 months old, will make them sleep like a rock all night. At 4 months old, their digestive system is not even fully developed yet.
What I would do is, burp her more often. Perhaps.... air/gas is making her "full" thus she only takes in only 3 ounces at a time. Or try a bottle that does not accumulate air bubbles in the bottle as the baby drinks.
4 months old... is still really young. With both my kids, they both fed every 2-3 hours at that age and older. Normal. AND they woke and fed more often when they were "cluster-feeding" or had spurts of growth/developmental changes/and hitting milestones. Normal.
I think, your baby is doing fine. She is feeding consistently and signaling when she is hungry, which is good, and at least she is not over-feeding and/or getting reflux. But, try asking your Pediatrician. But to me, well... that is normal baby behavior. Both my kids, at that age, woke at about the same times. ESPECIALLY at developmental changes and growth-spurt periods... this is when babies wake more. It will pass.
And like Jennifer S. said, both my kids did not sleep through the night either... until about when they were 2 years old. This, is a common natural pattern and progression in a child... per their development. But.. each child is different.
All the best,
Susan