Her weight is just below the 10th percentile for her age. Her height may have an error or she really is very below the 3rd percentile. Did you mean 30 inches for her height? Children need food to grow and energy due to being very active. She needs approximately 850 calories a day, based on her current weight. As a guideline for a 12 month old child should eat the following: Dairy 3 feedings a day – Milk (4oz), cheese (½ oz), yogurt (½ cup), or cottage cheese (¼ cup). Starch 4 feedings a day – Cereal (¼ cup), pasta (¼ cup), rice (¼ cup), bread (½ slice), or crackers (2). Fruits & Vegetables 4 feedings a day – Fruits (including 100% juice limited to only 4-6ozs) & Vegetables (¼ cup). Protein source 2 feedings a day – Meat or fish (1oz), egg (1), or beans (¼ cup). She should eat 3 meals and have snacks between meals using the foods above to be spread out throughout the day. Suggest eating meals with your daughter as a family so she is less tempted to want more food. Hoped this helped.
Sounds a little like my daughter has always been. Her appetite increases and decreases with her growth spurts though. Your daughter just might be getting ready to grow and her body is preparing her for the spurt. I have never denied my children food if they asked for it (good nutritious food that is). I limit the sweets and cookies and stuff. When my daughter was around the 12 month mark, she would eat her oatmeal, an egg and a whole banana for breakfast (not a small banana either), and sometimes toast too! My mother in law couldn't believe it! She still eats a big breakfast like that at 2 yrs old. She'll typically eat a whole package of the quaker instant oatmeal (which in and of itself would fill me up!), an egg, and some fruit. Lunch and dinner are typically smaller though. She'll typically have one or two more snacks during the day (crackers, fruit, cheese, yogurt, etc..). My daughter has always been very tall for her age, and has always carried a little extra chub too even though she is very active. She is always 100% for height and weight for her age group. I think her appetite will eventually slow down, and I am already seeing her slim down a bit... even though she still has a round belly :-) I'm not going to worry too much about it until she is out of the toddler years.
I guess the only thing I would suggest is that when you feed her a meal, you eat your meal at the same time. So that way you minimize her wanting food simply because she sees you eating something. Both my kids are like that too. I could have just fed them a huge meal, but if I decide to indulge in a cookie or cracker or something because I didn't eat as much as I should have (because I'm so busy trying to feed a 2 yr old and a 1 yr old)...they will want exactly what I am eating too. If one person eats, the rest of the family wants it too.
My philosophy is that babies are growing so much that we shouldn't deny them food as long as it is healthy, nutritious food. Make sure her snacks are healthy too, and then you shouldn't have to worry too much about the fact that she seems to want to eat a lot.