Is it immoral or unwise to accept a better job soon after starting a different one?

I am ready to change jobs. I could probably move to another role within my company pretty quickly and easily and continue to move my career forward, but I could make more money and get better experience outside of my company. Outside job hunts can be lengthy and full of disappointments and all the while I would have to work at a job that is, frankly, killing my soul. I think it's pretty clear that -- if I accept a new job in my company and immediately turn around and give notice to go somewhere else -- I run a high risk of burning bridges with key contacts at my current company. But would it be unethical in some way to do that? When you accept a job are you making a tacit promise to work there for some period of time? If so, what's the minimum amount of time?