So, so common. From 9-12 mo, Tyler ate NOTHING, I mean NOTHING, from a spoon. Yes, he was on formula until 12 mo so he was getting proper nutrition, but it drove me bonkers. He finally came back around to eating with a spoon again at 13 mo or so, and I had his iron levels checked right before that (after about 1 mo of no cereal or formula). You know what? They were fine. If you're concerned, you can always ask the dr to check them at her 1 yr visit, and he/she can always prescribe an iron supplement if it's too low.
In the meantime, your best bet is to go with the flow and sneak in some iron where you can. Cheerios or other iron fortified adult cereals are good, and I used to coat fruit chunks in dry infant cereal. Other good sources are wheat germ (stir it into yogurt or purees), beans, tofu, egg yolk, and a whole list at this website:
http://www.wholesomebabyfood.com/Iron.htm Also, vitamin C helps the body absorb iron, so offering a vitamin C food at the same time helps too. Oh, and I used to stir at least a little infant cereal into anything Tyler would eat from a spoon once he started again...yogurt, baby food, you name it!
It's okay to just let her feed herself finger food, and offer the spoon on occasion to see if she's warmed back up to it yet. If not, no big deal. It will be a loooong time before she learns to eat with a spoon herself, and allowing her to exert her independence and eat finger food won't hinder that at all.