I have 2 under 2 and they both eat well w/o issue, no food throwing, no refusing to eat what is served. The behavour of throwing food is a learned issue when they get away with it. Mine attempted to drop food on the floor for the dog or to directly feed the dog. This resulted in their getting their food taken away and offered to them one bit at a time. They would rather feed themselves so they did not like this at all. If they threw a temper tantrum, I turned their chairs to face the wall, if the tantrum continued they got placed in a play pen in a room alone. At first they would scream and scream b/c they did not like to be alone, they are used to being with their 7 brothers and sisters at all times. I kept with the program and the tantrums stopped as did the feeding the dog or dropping food on the floor.
With consistancy (A LOT OF IT), it does not take long to win this little battle. It is better to learn limits now than to have a teenager without limits. Then you are in real trouble.
YES, start her on vitamins and don't let her play on your sympathies IF SHE decides not to eat. Sometimes a child is more strong willed than the parent and wins. Let's face it, NO ONE wants to feel they are starving their little angel or listen to them scream forever. BUT none of mine have starved and they are all very well behaved. Don't give in, buy some earplugs if need be. Just take her food away and offer her one bite at a time. Children will NOT starve if food is offered, even food they don't like. I have a steadfast rule that you eat at least one bite of everything on the table, no matter where you are and no matter whether you hate it or not. No one is going to die from one bite. Thet are also required to eat what I cook, not something else. I cook 3 meals a day. Everyone gets to pick their favorite meal every week, without picking the same meal 2 weeks in a row. They have to pick 4 different meals in the month. So our diet is has a lot of variety and what one them likes, someone in the groups is going to absolutely hate. BUT they have to eat it anyway. Same rules for everyone. I have raised a group of kids (and grandkids) that will eat anything. But it took and still takes (with the babies) a lot of "sticking to it" to get it done.
Good luck with whatever you choose to do. I know what works for one family does not work for another. I have kids come to my house that only eat pizza and Mexican Food. The do eat what I cook though, but never at home. Their moms are amazed. LOL