Publishing with/without advisor as new Master student
Don't be shy about pushing your work forward. The stage at which a person becomes able to do original research is not fixed. Some people are more advanced. Well done you.

Generally speaking, a single paper isn't enough of a benefit that it should cause you to burn bridges. So I suggest you scope out how the faculty in your department would think about such an idea. 

Your option 1 could get some feathers ruffled. Your option 3 seems to needlessly delay your advancement.  

I suggest you find some variation on 2. In the school I did my PhD there was a head of graduate studies in the department. You could ask that person for some guidance. Present it as wanting to satisfy both being a good member of the university as well as advancing your work.

It isn't necessarily the case your department will push you to have a co-author. If you have come up with the topic and done the work entirely on your own, most profs will agree you should publish it as the only author. 

It's different if you have any kind of assigned supervisor. Even if it's a very distant and high level kind of thing. For example, maybe there is one prof who deals with all the masters students. In that case, you would still want to approach that prof and discuss how to proceed. Still frame it as wanting to be a good member of the university while also advancing your work.