Flying With a 6 Month Old! Help!

I need major help! My husband, baby, and I are flying from DFW to Florida in May and we will be traveling with our 6 month old (4.5 adjusted born at 34 weeks). I have flown a handful of times and I hate airports! Not the flight itself but the presence of being in an airport is over whelming to me. What do I do with her car seat? Stroller? My parents are driving there and checking in the day before us. So I may send her with our back up car seat and stroller and leave ours in our car at the airport because I plan on holding her the whole time and baby wear through the airport. She’s a really good baby very quiet so I imagine she will sleep the majority of the time. Does her diaper bag count as my carry on? Or do I get my carry on and her diaper bag? Am I allowed to bring her can of formula? I know I can buy water once I’m in the airport to take on the plane. Any tips or input is greatly appreciated!! Here’s our little chunk!