This won't be the answer you want but, you'll not be suprised if you've been reading any other threads here. The answer is it depends. I've traveled with my almost 2 year old and been allowed to bring a sippy of milk through RDU but had to pour it out in BNA and BOS.

One trip was back before the secure area liquids were allowed on planes. Then I could pour milk from a bottle purchased after security into a sippy and that magically transformed it from a liquid capable of bringing down a plane and worthy of a diversion into a no threat liquid. Those sippy cups are amazing things.

You probably will find milk for purchase in most airports after security but don't count on it being whole milk and certainly not organic. Be sure to explain to your toddler that this is making him/her safer.