Hi L.,
like one of the other mom's mentioned, the things she likes are mostly high-fat, fried, processed, and unhealthy--and YOU do the shopping. Her body is so small right now and she needs all kinds of nutrients to help her grow. You won't find those nutrients in chicken fries and hot dogs.
If you take her to the grocery store with you and let her pick out fruits and veggies, she will probably become more interested in them (talk about what colors they are, the texture). Let her hold some carrots, some celery, etc while she is in the cart. She will become familiar with them. If you don't buy unhealthy food, she can't eat it. This is a great time to help her learn HEALTHY eating habits that will hopefully stick with her for a lifetime. Like another mom mentioned, let her help you in the kitchen--let her wash the veggies, make a sandwich, etc. At meals, talk about how milk helps you build strong bones, veggies keep us healthy and help us not get sick, etc.
Although I read that one mom said it can take 3-5 times of introducing a food, it can actually take about 12 times before they will try it or like it! (info form Parent's As Teachers and other research). So, don't give up! Your taste buds adapt to the kinds of food you eat. If she only eats these high-fat, fake foods, that is what she will learn to like. If you continually introduce healthy foods, she will learn to like them. As she gets older, you will have less and less control over what she eats. Right now, you still have a lot of say in it. Start her on the right path and your job in the future will be much easier.
I also believe you are not a short-order chef. If she doesn't want to eat what you have fixed for dinner for EVERYONE then she can eat it the next time she is hungry. If she learns that when she says she doesn't like something she'll get a hot dog instead, she'll never try anything new. And for a little encouragement, I have worked for many years at child development centers with toddlers. At meal times, they know we don't have anything else to give them if they don't want what is on their plate. It is just not an option. Over the years, I have never had a child refuse to eat what we give them and ask for something else. They at least eat something from their plate and we encourage them to try something else. Meal times are not a struggle--even for 8 toddlers at a time. Most of them even eat their veggies!
Also, an excellent book to read is "If It's Not Food, Don't Eat It" by Kelly Hayford C.N.C. I started reading this book after my husband had cancer last summer (age 26) and it talks about all the unhealthy additives, artificial colorings and flavorings, preservatives, and chemicals that are in todays food of the Standard American Diet (S.A.D.). It's entertaining and very informative. It will help you have a healthier lifestyle and will effect the way you feel (more energy, less fatigue, less illnesses). As someone else mentioned, I also have the book "Deceptively Delicious" by Jessica Seinfield. It is a great book, but just remember that in addition to "hiding" healthy food, you have to continually introduce it as a healthy side dish or snack to your child.
Hope this helps (sorry so long) and best wishes. Let me know if you have any more questions on nutrition, I have a lot of info on it.