Too early for baby oatmeal?

My son is 2 months old and I just gave him half an ounce of baby oatmeal cereal mixed with formula. My mom started me on rice cereal when I was 3 months and I was a premie, much smaller than him. I'm only doing this because he eats 5 ounces every 2 hours and at night he'll cluster feed every 45 minutes and I haven't slept! Is it too soon? Or small portions okay? I just want to help him stay full longer at night

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