I did with my first daughter. She was a couple months old when my wife and I took her on her first flight to Texas for a funeral, then back again a month later when we had already purchased tickets. She did AMAZING. Everybody commended us on having a great baby that didn't fus, and we made sure she was drinking a bottle or had a pacifier as we took off so that her ears just didn't "pop" at altitude. No problems. We also took her on a flight when we went to Florida and she was just as amazing.
Grab a stroller and use it throughout the airport. You DO NOT need to check it in at the counter. You can use it through security and you do a quick residue and/or pat down at security. They don't make the family go through the scanners.
When you get to your gate, check in with the counter to make sure you grab a tag for your stroller if they haven't given you one at the check-in counter before security. If your infant is in car seat that attaches to the stroller (like the one we used when she was an infant), you just have it attached to the stroller and make sure to get a separate tag for that as well. When you get right to the plane (before entering), you take out the car seat and fold up the stroller. You place them right at the area in the corridor just right before it meets the door to the plane (they'll explain). As soon as you get off the plane, and in the same area corridor, they'll bring you your stroller and seat (if you had one) so that you can go about your trip.
My youngest, we have yet to take her on a plane, and I am afraid to do so as she is very active and doesn't like to sit still. For a 3 month old, you won't have much of a problem so long as you have something to entertain her if she likes to stay awake. If she likes to sleep, then make sure to keep a bottle or pacifier to sooth her while she lays in your lap. Children under 3 is free (on lap). If you want their own seat, then you pay the ticket for the seat and make sure to bring on the car seat.
My oldest daughter has been on a plane a total of 6 times, to and from Texas and Florida. Never had a problem with her. Be sure to bring snacks, little toys, and food for the baby, as well as diapers.