Hey V.! I remember when I went through this with my little boy, he's 4 now. I'll tell you how I was told to do this & it worked for me so maybe this will work for you too. Good luck!
Usually "around" age 1 you want to start introducing whole milk, either in a bottle or sippy cup. But, YOU DECIDE when is best for her to be introduced to milk b/c you know your child - if she's eating other foods really good & she's not under weight, usually after a year old is fine. *** side thought - Contrary to popular belief children really still need the fat content from whole milk even after age 2, unless they are overweight. (just a thought)
I started putting just a little amount of whole milk in my baby's bottle with the rest of it being formula. For example, if your baby is drinking an 8 oz. bottle, start by putting about 1 oz. milk to 7 oz. formula. As she gets used to the taste over a few days gradually add more whole milk - the amount of formula she gets will be less & less over time. Then before you know it she will have made the transition slowly & gradually ... she probably won't even notice the change by then. It's easier than it sounds. :)
Just a thought about the table food - you may be doing this already - but you may want to just do a thicker puree or mash up some of the food that you've already cooked for the rest of the family. This way she's getting a taste of the table food without the fear of getting choked or coughing. And like someone said, it may be the texture of the food.
I hope all this helps. Have a WONDERFUL day! :)