3 months/12 weeks, give or take, is a HUGE growth spurt. Babies normally need feeding far more frequently for a few days till either mom's milk supply adjusts or their appetites level off with the new feed amounts if bottle-fed.
If this is a normal growth spurt, I'd consider not doing the rice. It makes the feed thicker so it stays down better, but agree with PP about gut development. Keep an eye open for anything unusual tummy-wise: gas, discomfort, weird bowel movements. Grain carbs are pretty complex for little tummies to process.