Meet with another professor in our university to discuss a paper that I wrote and her student is co-author with me Recently, I wrote a draft paper based on the results, which I prepared for final project of one my courses (I'm a PhD student). In fact, I had a project partner in that course and I thought I should put her name in the paper as well.

I know it was just a short project and I did not mean to submit it to a really high impact journal (I mean I want to submit it to Computational Materials Science journal, impact factor: 2.530). Also, my PhD adviser was one of the instructor in that course.

Today, I just sent the draft to my partner and said please read it and let me know if you want to add or modify something, but she responded back that her adviser wants to meet me and discuss the work that we did. In fact, she said her adviser does not want to be on the paper as co-author but she wants to be sure that there is nothing in the paper which may have bad impact on her.

The question is: I'm not sure it is an appropriate thing to do (meeting with another professor)  without consulting with my adviser?

I said I should consult with my adviser before meeting and know his opinion. Should I talk about this with my adviser or just give it up at all? Because I don't want to make everything complicated about who should be co-author, etc just for a small side project. Any idea or suggestion is appreciated.
It is typical for advisors to want to help emerging PhD students in their efforts to publish papers. Typically, advisors can give a paper a rudimentary review with little time or effort. You would typically recognize this support with an acknowledgement, not coauthorship (in the fields that I am familiar with).

This seems to be in line with what your coauthor's advisor has in mind. I would take the coauthor at their word regarding the fact that the advisor does not wish to be a coauthor. 

In addition, you do not want your own advisor to be in the dark about this paper. It is good that you have presented it to him at a prior occasion. Prior to meeting with the coauthor's advisor, you should email your advisor about the paper and let him know you are preparing to submit it. Depending on schedule/your needs, your advisor will likely be willing to provide a brief review of the paper. If he does, he should also be expecting an acknowledgement, not coauthorship.