Abnormal appetite in toddler?

I am really worried about my 18 month old daughter's appetite and eating habits. I hear all the other moms I know saying that their toddlers are such picky eaters, but my daughter will eat anything you put in front of her. What I worry about is that she always acts like she is starving even if she has just eaten a full meal. If she sees someone eating something she will scream and have a tantrum to get some even if she has just eaten. I prepare her very healthy foods and she eats 3 meals and 2 snacks per day. I know you are supposed to let your child eat as much as they want and they will naturally eat until they are satisfied and stop eating but if I let my daughter do this she will eat until she gets a stomach ache. One morning for breakfast I tried letting her eat until she wanted to stop and she ate 2 scrambled eggs, 2 whole slices of wheat toast, 1 whole banana, and 10 oz of milk before I took her plate away and she still screamed and threw a tantrum like she was still hungry! She is not overweight at all and in fact she is pretty small for her age so her weight is not a concern right now. My fear is that when she gets older and starts school and begins eating meals away from me and her father that she will make herself ill by eating so much. I have discussed my concerns with her pediatrician and she says that I should not worry. She has had blood taken for thyroid levels, electrolytes, iron levels, and blood glucose and everything was normal. I still can't help but feel that something is not quite right. Do any of you have a toddler that does this? Any advice?