Should I switch to mostly pumping?

Hi all,

I have a 4.5 month old that although is very healthy he's still pretty small. He's at about the 15th percentile for everything and just weighed in today at 12lbs. To be fair he was 7lb6oz when he was born which is smaller than my other two kids by over a pound. The doctor did mention that maybe it's time to start giving cereal to help increase calories. He's always had breastmilk and is still nursing but does get a bottle while at the babysitter's. He seems to be a distracted eater and will fall asleep or just start smiling and pulling off. He rarely goes more than 1.5 to 2 hours before being hungry again. I'm wondering if maybe switching to pumping and giving him bottles will help with weight gain since he won't get too distracted during a bottle like he does when nursing. I'll also add that he sleeps great at night so I'm not looking into this solely to get him to sleep through the night. Any help of input is appreciated!