every child is different. If she is showing interest, why not try it?
My little one is WAY ahead of the game. He's had some health issues, and has Reflux, so we stared with rice cereal blended into his bottles at about 7 weeks. After a week and half, he got too constipated, and the doctor suggested we switch to Oatmeal. He has no problems with that. Now, as we are introducing a medication to treat his reflux, the doctor has recommending mixing the meds into a tablespoon of applesauce and adding some breastmilk to it..and serving it with a starter infant spoon.
we tried this for the first time tonight (at 10 weeks) and he was SOO happy. He loved it! He got mad when the spoon was NOT in his mouth, he wanted to suck on it like a nipple. I don't plan to introduce any other foods besides his cereal and the applesauce for meds until about 4 months.
However, I never suggest replacing breastmilk with solids that early. It's still very important that they get plenty of breastmilk. So if you had one serving of cereal per day, I'd suggest feeding her shortly before you expect her to be hungry to breastfeed, then you can easily follow the cereal with a nursing.
I worked in the infant room of an early education center, and I learned that every child moves into solids at their own pace. Some loved cereal and breastmilk on a spoon at 3 months, others went straight to thicker cereal with foods in it at 6 months. I would suggest waiting on finger foods until they can sit up in a chair. Veggie Puffs are a great starter. They melt easily in the mouth. :)
Good Luck!