Fortunately for you 3 month olds still sleep a good bit! :)
Pack in carry on for baby (diaper bag):
diapers (1/hour of trip)
package of wipes
2 outfits (1 in case child spits up/pees/poops and 1 in case luggage gets delayed)
couple pacifies (if you use them)
1-2 small toys (things to look at/chew on/rattle/etc)
hand sanitizer
Pack in carry on for you:
change of clothes
hairbrush
hairbow or ponytail holder (if you have longish hair)
toothbrush & travel sized toothpaste
chapstick/lip gloss
book/magazine for when baby is sleeping
cell phone & charger
wallet with proper id/passports/etc
car keys for when you return! :)
Hint: if you roll clothing items 9as opposed to folding them)it saves space and reduces wrinkles
Security issues:
Get to the airport at least 1.5 hours before flight (ie parked and inside main doors)
If you can print out your ticket at home do it (there is a kiosk for those with tickets already so you don't have to stand in line to get your ticket and have bags checked)
Be prepared to show items in bags
Wear easy on/off shoes as you may be asked to remove them when going through the security check point
Other than having to wait in line it shouldn't be a bad experience :)
Enjoy your trip :)
Adhere to airport rules on what's allowed for carry on items - check airport website for details