There are many reasons why it is helpful to publish. The usual reason is that it enhances your standing in the community of scholars and professionals. But another important reason, in my view, is just for the experience of it. You force yourself to bring your ideas into an understandable and maybe usable form. That is good for your mind and publishing is just the goad to get it done.
Submitting to a conference or journal will also get you independent feedback on both your ideas and your writing. That is valuable also.
In CS, however, most of the work is presented in conferences, so you might look for a suitable one and submit there.
If you want a career in academia, publishing is essential, and starting early gives you more experience for when the more important results are ready.
It is also usually good advice to follow your advisor's lead.
Good luck and see you at the conference.