My mother had a similar situation with my brother up to his teen years. He would fixate on one food or food group and that would be it. He went through the dry cereal stage, the soft-boiled egg stage, the hamburger stage, you name it ... The pediatrician recommended a vitamin supplement and to keep putting other foods on his plate (whatever the rest of the family was eating) but to ignore his response or lack of to the new offerings. Sometimes, he would see us enjoying the "new" thing and would cautiously try it on his own. Funnily, this would occasionally lead to new stages, the carrot stage for example, but this low/no pressure tactic worked. He was one of those kids that if he felt any pressure to eat something he decided he didn't want, he'd vomit.
Another idea, even though she's so young, ask her to "help" you cook, even if it means just pouring cereal (pre-measured) into her bowl. Maybe if she's involved in the process she'll want to taste-test her creations.
I like the idea of substituting muffins for cupcakes. Quick breads such as banana, carrot and zucchini make great muffins. Top them with a dab of Cool Whip might be even better. Also consider ditching candy and cookies and substituting better things like fruit chews and chewy granola bars. You can also find good and easy recipes for your own bar cookies using oatmeal and fruitspreads or applesauce.
Don't be discouraged. With perseverance, this too shall pass. Good luck.
(My brother's pediatrician's outlook was at least the kid was eating.)