Traveling at this age is comparatively easy peasy. I would try and time our flights around when my son normally napped. I would nurse him on the way up, he would conk out and then before landing he'd wake and I'd nurse him again. It wasn't bad that way. If she takes a bottle, then I'd just be sure to take enough formula with you. Check the web sites. I think they've made exceptions for mothers traveling with babies, but I don't know what they are.
Pack a few extra diapers in case of delays. You can change the baby in the airplane lavatory, or if it's jsut a pee diaper, on your lap (sometimes that's a lot easier). If she takes a pacifier, bring that along too. If you're not getting her a seat, wear her in a sling or the baby bjorn during the flight.
As far as what to take, etc. You can check your stroller and car seat at the gate. I found taking the stroller made it easy since you can load these up. Give yourself a little extra time to get through security. It sounds like you're traveling with your dh, so that will help. I always traveled alone for some reason but did just fine.
Love Field is pretty good. They have a family lane if I recall correctly. They've eliminated the family pre-boarding, so print your boarding pass the day before online. If you don't make it into group A, it's no big deal. You get to board after the A group, and before the B group. Everyone is really helpful too. American offers no pre-boarding whatsoever anymore. Personally, I prefer SWA since they're more flexible as well if you need to reschedule.
Good luck! Traveling with a baby isn't bad at all. It's when they get older it's more of a challenge. Enjoy the trip!