Yes, toddlers can be picky!! My son did not care for meats either and I wished he would eat meats! But it will come, gradually, with time. I second the advice of allowing dipping sauces - kids LOVE to dip. My son "magically" started eating stuff he would not even touch before once he could dip veggies into salad dressing, other stuff into ketchup, he LOVES sour cream (my husband and I joke that he eats his (whatever) with his sour cream instead of the other way around!) and all that.
Also, if she doesnt like something, that's ok, maybe she will like it later when she is bigger. We do have a rule that he has to take 3 bites, first to try, second to taste, third to decide. Then if he truly doesnt like it, ok, maybe later! My son is a good eater, he can be just as picky as any other child but he knows he has to have that 3 bites (or since he is 6, he has to take 6 bites + 1 to grow on - he's a skinny little kid) The only thing he truly does not like is fresh tomatoes, that is his thing he doesnt like now but will like when he's bigger (he says so every time now when we have tomatoes. We respect that, smile and say, yes you will like it when you are older.)
Little kids really do get by on so little food, so just because she only ate a bite of a chicken nugget doesnt mean she isn't eating *any* meat. Just offer plenty of healthy foods and be mindful of the protein that she needs to get more of in other foods like beans and cheese and eggs (and yes peanut butter.
I wont argue with your pediatrician, not knowing whether there is a specific reason for your daughter to wait till 2, but I will say that I read not long ago that they are actually now finding that the OPPOSITE is true, that giving your kids common allergenic foods earlier instead of waiting longer MINIMIZES the odds of being allergic to that food later!
Moderation in all things though! Dont suddenly start giving her peanut butter sandwiches for lunch, peanut butter spoons to lick for snack, peanut sauced noodles, all that - overdoing it is probably MORE to blame for allergies than the age of first exposure.)
My son hated peanut butter. Wouldn't have a thing to do with it. Darn, and I was trying to fatten him up cuz he is sooo little. (MY pediatrician actually said to put butter on everything he ate. That backfired big time and besides, I wanted him to gain weight on FOOD, not FAT. Consequently it took 2-3 years before he would accept butter on bread, toast or pancakes!!) Anyway, back to peanut butter - my son would not eat PB, and in Kindergarten, they had lunch last (they had mid-morning snack) and I did not want to send ham sandwiches etc that needed to stay cold cuz I didnt know if it would still actually be cold by lunch. So I got Nutella (hazelnut chocolate spread, MMMM yummy!) and he loved it. Throughout the year, I gradually increased the amount of peanut butter I mixed into it. Now he will finally eat PBJ sandwiches (not his favorite, but he will eat it).
Anyway, that was quite a digression, sorry about that!
Chop up meat (ham?) really small and mix it in with bits of her other favorite foods (veggies? cheese?) in a cream cheese base and spread it - call it confetti spread or something like that. (My son loves "Rainbow Sandwich" which is simply pink ham, white spread, green lettuce, yellow cheese... It's all in the name & presentation sometimes -well, most of the time I think!)
Something my son ate surprisingly well when he was a toddler was stir fry which we ate often. He loved the yellow/red peppers (!!) raw OR cooked, he loved the rice (oi, so messy but...) broccoli raw or cooked, carrots, etc etc. and after a while, he'd start eating the small chicken pieces since it was all blended in and sauced up. Only a small portion of his (still very small) meal would be meat as an older toddler but now he is normal as can be in his eating habits.
Your daughter will love hamburgers soon enough, so be glad she's eating veggies, fruits, whatever else that she's eating now.
Oh and dont get me started on little kids being vegetarians! TEACH THEM THAT SOME ANIMALS ARE RAISED FOR FOOD! Americans are sadly way too dissociated with our food sources. Yes, chickens have bones and no there aren't any chicken parts called "nuggets" Just be matter of fact about it. It's not like you're eating the family pet, dont even compare it to that. To each their own though!
Tofu is another thing you could use, I dont remember if it is "equal" to meat, but make lasagna or stuffed shells (that uses eggs too, she wont know!) with tofu. (My husband does not like eating anything that he cannot recognize in its natural form, so we dont eat much tofu, but I've cooked with it before and it tasted ok to me.)
Another thing, I know you're asking about meat, not milk, but that was something my son never would drink (and neither does my husband, so I didnt push it). I just made sure they got a lot of dairy products in non-milk form, like yogurt and go-gurt and make my own popsicles out of smoothies and such.
Bottom line, just watch your daughter's overall consumption of foods and as long as it balances out by the end of the week, it's fine. (sorry, another story here. My mom said I bugged my grandma (and she my mom I'm sure) when I would ONLY eat one thing, like broccoli, off my plate at dinner. The next night, I ONLY ate the rice. and so on. My mom said by the end of the week, my diet was balanced!