I wouldn't worry about her becoming malnourished, as bananas are a great source of vitamins and minerals (my dad made us eat at least one banana a day for that reason!). And unless your DD is eating over 10 bananas in a short period of time, theres no threat of hyperkalemia (excessive potassium) as the digestive system filters it out excess potassium before it becomes a problem.

I can't really help much with getting her to eat more! Though if you're worried about nutrients and her weight, maybe you could try her with a mango, banana and orange juice smoothie, which has lots of good energy and vitamins