Hi, M.. Well, I don't think there is a problem with a baby consuming rice or rice products. All grains have starch in them, so no matter what grain product she eats, she's going to get some starch. Unless she already has a weight problem, there is probably no need to be overly concerned with her weight in the near future. The stuff that truly makes children gain weight are emtpy calories with no real nutrition in them -- such as drinks with no real fruit juice that have a ton of sugar in them and little else besides food coloring. Unless your doctor has told you to be very careful to keep her from gaining too much weight, then what you want to do is just give her nutritious foods that she can digest without discomfort. Sounds like you're doing just that. At this point in her life, she is going to gain weight rapidly at times of growth spurts and then gain slowly or not at all at other times. She's probably not going to have a really smooth, gradual weight gain. Kids usually don't grow like that. Keep sugar away from her as much as possible and feed her healthy stuff.
Since she seems to do OK on rice, I don't think you should eliminate the rice cereal totally, especially if she likes it and does well on it. If you want to introduce oatmeal, do it a little bit at a time. Oatmeal has a lot of fiber in it which can affect her bowel movements. Some kids don't do well on oatmeal at all. Try a couple of spoonfuls of oatmeal, see how she does for a couple of days, and then if she doesn't have a bad reaction to it, she can have more. Oatmeal has gluten in it, which I don't think rice does, so there is potential for allergic reactions with oatmeal along with the changes in bowel movements because of the fiber.
Oatmeal also gives kids and adults a lot of energy, so you may find her somewhat more active on oatmeal than on rice cereal.
You might want to forget about oatmeal at 6 months and just keep her on rice cereal for the time being. You might want to try oatmeal when she's a little bit older and has a more developed digestive system.
Peace and good health,
Syl