Am I betraying the people who promoted me if I leave?
No, not at all.
You are currently selling yourself short. While loyalty is valuable, it's a one way street. They are only as loyal to you as their funding permits and their program exists. At that point they cannot and will not be thinking, "we are betraying you." You knew what you signed up for when you applied for the job. You deliver your work, they deliver your pay and that's the end of the transaction.
They will be able to find someone else to replace you. Sure, they'll be worse off than if they had you, but if you constantly try to please others at your loss, you will make some very bad decisions as life goes on.
A business relationship has to be of mutual benefit. If one party or the other is unhappy, or can get a better deal elsewhere, then the relationship is due to be reworked or dissolved.
If you really enjoy the work, if you're going to get more out of it than you're putting into it, if it will lead to something better soon, then maybe you should consider staying.
But as far as I can tell you should give them two weeks notice, tell them you'll be happy to respond to email and phone questions, and move on. They will manage just fine, and in fact you'll be opening a spot for someone who, like you did some time ago, needs that job but wouldn't qualify for the better job you're about to take.
I know it's difficult to leave your comfort zone, and you naturally feel like you're hurting someone when you leave, but this is part of growth.
Don't deny yourself this opportunity for real growth.