The first step to making this easy on yourself and your child is to mentally prepare them in advance. Whether this is their first trip or not they are going to be excited and anxious to be on an airplane. I usually purchase an airplane type toy for a toddler or download music or a movie for the child 1 week before the airplane takes off. During this week, I take my child through the process of packing our luggage, driving or taking a cab to the airport, unloading our bags, checking-in, going through security, walking through the terminal, going to the boarding area, boarding the plane, going to the bathroom, buckling your seat belt, taxiing on the runway, and taking off. It is important to understand all of these steps as you want your child to remain calm and comfortable for the entire flight. If your child knows what to expect he/she will act like they have been there many times before.
You are not the only one with luggage. You should have a small piece of luggage for the child that can fit under her seat. It's a bonus if the luggage has handles and wheels like yours. Your child will feel independent and responsible with their own bag. In this bag should be: a DVD player with 2 movies that were agreed upon before the flight, a change of clothes, coloring books, cheerios, fruit, and a cup with a lid on it. As soon, as you walk up to boarding area go to the desk and let the flight attendants know that you have a little child with you on the plane. This will give them a chance to let the other passenger sitting in your row that there will be a child. It also allows you to board the plane first and if you haven't had a chance bring your child to the bathroom. You should also see if there is another child on the plane and if you can sit closer to that family so that your children can play together in a row.
Enjoy this time with your child as it is a memorable experience for them. They do not know what to expect and traveling by airplane can become hectic when you are doing it alone. Imagine how crazy it can become if your child begins to throw a tantrum or wants to touch and see everything in site.