Hi there - I have an "old school" pediatrician, meaning he advised that we introduce solids at 4 months (that's how babies in the 60s and 70s were raised - and we turned out fine). And, he suggested that we jump to fruits and veggies -not start with rice cereal. He also said 4 months or so was okay for us to introduce just a few ounces of apple or other fruit juice a day (however, my baby at 8 months, still does not like the taste of juice).
Rice cereal tends to constipate. I would suggest introducing foods that soften stool first - e.g. prunes definitely, pears and peas - before moving on to applesauce and sweet potato (foods that can constipiate). I believe BabyCenter.com has a list of foods that constipate vs. those that don't.
According to my doctor, 6 months is definitely old enough to try juice out - prune juice for your little one if you're afraid of constipation. I would only be concerned about the BMs if it's a sudden change or if there's blood/mucus - e.g. your daughter used to go every day and then suddenly switched to once a week. If she tended to only have BMs once or twice a week before the rice cereal, probably not a big deal.
I know it's easier said than done - but try not to worry too much. It seems like doctors or so overcautious these days about introducing new foods. Anyways, my 2 cents.