Well, the important issue here is what are YOUR thoughts about this?
Performing in front of others is an excellent exercise, and forces you to stop procrastinating in many ways. In that respect, setting a date and working towards that as a goal is an important part of learning a musical craft.
On the other hand, the voice can be a complex instrument to learn and to gain some mastery of. Since the voice is a very personal thing, it can be intimidating to sing live to friends, relatives, or strangers.
Some of that depends upon the difficulty of the material. Some depends on the stage of development of your singing voice. You may or may not be ready to take that plunge. When you do, success or failure, it's a moment of growth.
With our voice, we have so many moving targets to stabilize and get a grip on, sometimes it can take a considerable time before we can rely on new habits from our training to anchor those targets that try to keep moving. Once we get those things under our belt, it's time to start scheduling dates of one kind or another to keep our nose to the grindstone and our vocal development on task.
Public performance is a good way to hold ourselves accountable for our vocal progress.
What is the song? Any in particular or is your teacher just wanting you to get out there and do something for the sake of getting out there?
All the Best!