Hi N., did you know you can usually rent a carseat? I don't know if finances are an issue, but that might be a helpful option.
Don't assume you will get help from the flight attendants, airline employees, or that other passengers will be cooperative. If you don't get cooperation you will have to ask, and may need to be firm and insistent. Sorry to say that, but it's true.
Be proactive. Don't assume you will get priority boarding because you have a child. (Not all airlines are doing priority boarding for travelers with children anymore....which I think is totally wrong!!!! People end up separated from their mobile children and other passengers end up needing to move anyway!) Ask your airline in advance so you know what to expect.
The KEY is to get your boarding pass early, and arrive early. This will put you at a higher boarding priority and give you more time and choices. Print out your boarding pass online as soon as it is available to you if your airline offers that. This also saves time and eases the process at the airport.
Try to get a bulkhead seat. This is the seat at the front of the plane that has no seats in front of it. It will give you more room to handle the baby. There is a potential drawback however; you are not allowed to put the baby's bag, or your stuff on the floor or on the seat. You will not have storage in front of you (because there is no chair)and will need to fit your and your child's belongings UNDER the seat you are sitting in. The only problem will be if the person behind you wants to use it. Generally it's first come, first serve but it the flight is crowded they CAN make you move it. Most people would be reasonable enough to let you keep your baby's bag under the seat, but you never know. If you can't use the seat under you it will be stored in the nearest space above, and the flight attendant will have to help you get the items after take off.
Try to relax and have fun. Your baby will pick up on your tension. If she cries, just remember, babies cry, and if you worry about other people getting upset about it, you will just get more upset. Comfort and soothe her, meet her needs, and that's all you can do.
Have fun!!!! This trip is one that precious memories will be built on. Time goes by so quickly.