I have to wonder what exactly about this question is an "ethical dilemma". You feel some loyalty to your current employer, and that's admirable, but it's a question of an eminently more practical nature.
Some of the advice in this thread is not taking into account all of the possible variables either, so I'll share some extra stuff in the hopes it will be helpful.
I am going to assume only one thing here; that since you are applying to an "institution" for this new opportunity, you are applying to a place similar to where you are currently working, probably education and perhaps publicly funded as well. This assumption will play a role in some of the advice I offer below.
1.) Using an offer from a new employer is the worst leverage to use in trying to negotiate a salary where you are now. If you are going to apply, just do it, and if you get the offer, leave (unless the job raises red flags for you / seems like a bad fit). No matter what happens at your current employ (you negotiate more money or they offer it to you to stay) AND you stay, you will only ensure some of your colleagues end up resenting you. People talk.
2.) Be aware that if you turn down an offer from the new employer, you most likely will never get another offer from them again, for any position. You should be willing to leave your current position or write this new place off forever, basically.
3.) Most likely, there's a lot of cross-talk between these two places, being so close in purpose and location. My point being - again, if you are going to apply for the new position you need to be ready to accept that your current employer will likely find out about it somehow. They may or may not hold it against you in the future, especially if you don't get the new job.
4.) You work in a publicly-funded environment - one that (from the sounds of it) has a strong union, specific grievance procedures and salary based on time served. Benefits too. Make sure you are comparing apples to apples; don't underestimate the value of a government job. I'm not saying to sell your soul to them, but you should take into account ALL of the benefits, not simply the immediate financial gain.
5.) I have worked in so many different places, in so many different fields. One thing that's constant: if you work for or with unpleasant people, all the money in the world won't make that place any easier or better for you. Good people are worth their weight in gold! If you get bad vibes in the interview at this new place, don't ignore them. Pay very close attention. They may be the only clue you get as to whether or not you will be happy, at least in the short run.
6.) Using the rationalization that "they would cut your position in a heart-beat; why should you worry about being loyal" is an extremely poor justification for changing positions, or for any of your personal decisions or behavior, IMO. As I said above, this is not an ethical question; it's just a practical business decision, and one that people consider all throughout their career. So don't let it weigh heavy on you as some big moral choice - just logically weigh out the pros and cons, all of them, and act as you are best able to decide.
7.) 6 months in a new position is not a long time. It would make me wonder about your resume if it were to cross my desk - why do you want to leave so soon after a promotion? But, over 4 years there is a plus, so the likely outcome is neutral. IOW, it wouldn't stop me from bringing you in for an interview, but be prepared to answer questions about why this new position is so attractive for you, and why you are ready to bail from your current job.
Finally, as many other people have pointed out, if you feel all the pros outweigh the cons, go for it!
I wish you good luck and all the best.
which in all fairness, they do deserve that opportunity. don't keep them in the dark then leave, that's a shitty thing to do and it is likely to eat up a good infj's soul later on.
