I have flown many times with a pump. The flying part is relatively painless. As you are flying domestic, you do not have to worry about time difference, etc.
The main area you have to be alert is security. Your pump can NOT go through the x-ray. This means it should not go on the conveyor belt with your bags. It can go through the metal-detector archway thingy and, provided you remove any metal clips, it will not set off any alarms. The challenge comes if you are required to go through the human x-ray scanner (the big box in which you have to stand on the footmarks and hold your arms above your head). I have been advised by my healthcare team and pump manufacturer that the pump should not join you in this big box (some people say it is ok but i am not willing to test this theory). If you show your pump to the security team and explain, they should be ok. The way they handle it varies. Usually in the U.K., they ask you to remove the pump and will swab it as you stand with your hands in the air in the big box. If they offer to do this, they keep the pump within sight and give it back once you leave the big box. The other option (which they always do in the U.S.) is to pat you down so you do not have to wave your hands above your head. This may require some waiting around as there may not be a "patter-downer" of the appropriate gender around at the time.
I have never been asked for a doctor's letter. However, I always take one with me in case I need to show it to an over-zealous security person.
The only other thing I would mention is, if you are going away for a few nights, to make sure you have an alternative with you in case your pump fails whilst you are away. This may be the insulin bottle and a syringe, your old pens or some pump vendors may provide you with a loaner pump. And don't forget to bring a set change or two with you.