It is normal, but now is when they learn how to get what they want in terms of food, and what you boundaries will allow her to push. I would stop giving her any yogurt, bickies, bread ect... Whilst none of that is really unhealthy on it's own, if she is turning away meat or veggies and fruits in preference of those foods, and she's getting it, then she will totally stop eating healthier foods.
I did the same thing with DS1. He was fussy as a baby, and because I didn't want him to go hungry, I gave in and gave him yogurt or a sandwich ect instead of re-offering veggies/meat/dinner for him to eat. He is now 6 and a horribly fussy child. I dread dinner times because he won't eat dinner, but will complain he's hungry once dinner is finished. DS2 (although isn't naturally fussy) copies him, and it's just a horrible time of day for us, because I am trying tot each them they need to eat their meal, and won't get anything else. So they will then tag team nagging me to death for other food (usually fruit or a sandwich). Or they will throw tantrums and whinge and whine until bed time. I got myself into this hole, and it's proving to be tough going getting out. We're all suffering for it.
I would do what the others suggest. Offer her food. If she doesn't eat, don't worry she won't starve herself. My GP once advised me to look at children's food intake over a week, not a day. Just like us, some day's you feel hungrier than others. She will understand you mean business if you stick to your guns now, and not give into her demands for food other than what you've served her.