At six months it shouldnt be a big deal. I flew at 5 1/2 mos, and he did great. I bought a ticket since I was by myself, and wanted to be able to put him down. He slept the whole flight. I flew near naptime and kept him awake til takeoff time, gave him a bottle and he conked out. If I was with my hubby, I wouldn't have bothered with buying him a ticket. If the flight isn't full, they will let you take your infant seat on anyways. Just say that you want to "gate check" your infant seat and your stroller if you want to keep it through security and if there isn't space they will take it below for you at the gate. If you aren't alone and have a carrier you probably won't need the stroller, but keep the infant carseat. You will have to put the seat and the stroller through the scanner- big huge pain the butt if you are alone. I had a carrier and had him in that while I struggled to get everything through the scanner. Those items have to be upside down- ugh. One flight no one helped me and watched me struggle, so I just took my sweet ol' time about it. Another flight the security floaters were a big help. Make sure you go through the "familiy line" not the business quick-check line. Not sure what the rules are on shoes these days, but wear easy to slip off shoes if you have to take them off. I just had socks on my son, I don't know if they would have wanted them off too. They do when they get older. I got all of my stuff ready before I got in line, had my shoes off, baggy of liquids out, and carseat in a plastic bag so that it wouldnt get gross in the conveyor belt. Airports have family bathrooms and I was able to roll the whole stroller in it and lock the door, and change him on the stroller. You just have to locate it, there are only a couple.
If your breastmilk is labeled in a milk bag, they let it through. Food and formula is also allowed, food in the original containers. (or it was up til last year). Water is not allowed, but you can get bottled beyond security. If you have powdered formula in the bottles and buy water that is easy. Pack some food, a couple bottles, a pacifier, a change of clothes and some diapers. You shouldn't need much else. I had my usual small bottles of medicines and such that I carry in the diaper bag but had the liquids in my baggy of liquids. Give the pacifier or bottle during takeoff and landing to help the ears.
Check the TSA website and your airline's website for the most current rules about traveling with liquids and such. Go to the sections for flying with babies. Also, on my airline, they didn't count the carseat or the stroller as a piece of luggage, so I had my carryon, personal item to carry on, a suitcase, a stroller and a carseat.
Find out from your airline what is required to prove your childs age and identity- they check birth certificates or shot records usually. You will not be able to check in online with an infant, you have to go the regular counter at the airport.
I was terrified of being one of "THOSE" people and was so nervous, and really didn't need to be. People were helpful and they are very forgiving of infants. Now traveling with a 15 mo old, or a 2 yr old, that is a different story. Much more difficult because they want to run around. At 6 mos it was a piece of cake. Don't stress and have fun!