Daughter 2yrs struggles eating meat?

We struggled with this as our older daughter ate everything we put in front of her but our youngest would not eat meat from about 22 months to almost 33 months. She still is not real good about eating meat. We just kept on feeding her what everyone else in the family got. She would eat what she wanted and if she was still hungry, we have the "At least 2 bites" rule. Then we would give her other things to eat. Never a treat, but more veggies, or fruit or bread. Our doctor said her behavior was not uncommon and not to worry about it. He liked our rule and offered that kids that age will eat until they are full and then stop. She is petite, but healthy and has more energy that most kids.