i traveled with my infant on 8 different occasions (2 -3 legs with each trip...visiting family cross country), all before one year...i was breastfeeding, so i can't vouch for the bringing the liquids & formula as i really don't know (but we have been asked to dump water from a sippy cup before).
we always brought a diaper bag & another carry on each, plus a stroller (i was with my husband)...so one carry on was for adult things & the other for the baby, then the diaper bag. we kept the (smaller size) diaper bag stocked lightly with one outfit, 3 diapers & creams & such. i recommend bringing in your carry on plenty of diapers (enough for one day) just in case your flight is delayed (happened to us & apparently most airports only sell size 3 diapers) as well as enough clothes, wipes, etc for an entire day (we brought 4 outfits in the carry on & one in the diaper bag). we also brought along a wonderful toy: baby tad. it sings songs & lights up; it was priceless on all the flights & you can turn the volume down.
we found it okay to check the car seat...they wrap it in thick plastic & we never had a problem with it getting lost (but that is a concern). as far as i know, you are able to check the car seat at the gate. we always checked the stroller at the gate. i highly recommend not using a baby carrier/bjorn style exclusively b/c there may be times in between flights when you or whoever you're flying with don't want to hold the baby constantly (i.e. eating, in the bathroom, running for a flight)...
in general, it seems security are more understanding & lenient for folks with babies...then there was the time they had to search down the stroller, & my husband & i for some reason (they said it was b/c of the diaper rash cream!)...
i also suggest waking your baby up after you land & trying to coordinate naps on the plane. but if you have a no napper like we had, bring a toy that is mesmerizing for their age group! nursing or sucking on something while taking off & landing also seemed to help ease the ear pain...
another interesting fact: the food trays (two seats' pulled down at same height) work amazingly wonderful for a changing table. unless you know that the plane bathroom has a changing table, i wouldn't even attempt to change a diaper in that small room (been there, done that, doesn't work). it was always much easier on the food trays. we changed many poopy diapers on it & no one seemed to mind (thank goodness for hand sanitizer...). that way your not lugging you & baby & diaper bag through the aisle & then waiting for the bathroom, then discovering that it's too small to change it anyway...
another thought: when you are at the gate, go to the desk & ask if you can have a seat with an open middle seat & that especially works if you are flying with another person...that way you have all 3 seats (granted that they have a row of 3). most of the time that we requested this, they were able to help us out. it helps to have the baby in arms while asking!
if you must sit by another, it's always okay ask other passengers when you first get on the plane to trade seats so you can sit by your spouse or whoever...usually people are very happy to trade when a baby is involved.
as a sidenote: older men (say age 45-60?) seem to really enjoy sitting near babies for some reason! no kidding. all the women who were forced to sit by us seemed irritated the entire time, but the older men, all of them played with our baby & seemed to really enjoy it. just our experience!
dress your baby in very cute clothes & that also seems to really aid in the flight crews' adoration & help...seriously.
BTW: flying with an infant is really much easier than flying with a toddler!!! so i say go for it!