K.,
Your Pediatrician is right about the eating. Toddlers can survive on surprisingly small amounts of food. Don't let your child see that it upsets you or it could become a power struggle. And don't think your child needs a special, separate meal from the rest of the family. With the exception of very spicy foods or maybe sushi, she can have whatever you have, just chopped up well and not too hot.
Regarding day care, don't feel pressured to put your daughter in to "keep up." Taking her to the park or holding an occasional playgroup is plenty of interaction at this age. All they do is parallel play at this age anyway. Daycare will babysit her with lessons that are 1-2 minutes long because that is the attention span of the age. If you don't feel confident teaching, take her to the public library for lap sit storytime or enroll her in Kinder Music or something.
No one can replace you. You will get about 5 years with her and then most likely she will spend the majority of her awake hours with a teacher in public school. Now is your time to teach her lessons like unconditional love, importance of families, morals, ethics, values, etc. You will never again have her undivided attention and influence like you do now. Take advantage of it.
It doesn't mean that a child can't go to preschool for a year or two before Kindergarten. It is a great preparation in so many ways. But don't give those first formative years away to someone else full time (who will only be a part of your child's life for a year at best) if you don't absolutely have to. I taught preschool and worked at one of the nicest and most reputable daycares in town after graduating college and I can honestly say that daycare is highly overrated. No one tells you about the frequent illnesses, children's learned need for constant stimulation, direction and company (i.e. they don't entertain themselves anymore,) the stress on the parents both emotionally and financially. A decent daycare will cost you $850 a month or more.
I totally understand that some parents have no other option and daycare is a lifesaver for them. But please don't feel pressured to put your child in one just because you believe daycare can do a better job than you can. It simply isn't the case. Especially at this age, you can do more for your daughter than any daycare ever could.
Best wishes,
S.