My father is insistent that I talk to the woman who was my supervisor during my internship and ask her to get me an interview spot. I am not sure of their process for hiring, but I feel hesitant for doing this. I've never had to go through this before, and I am a bit introverted, but would this be okay to do? My supervisor for my internship was in a different department than the job I have applied for, but it's a small enough nonprofit where they are basically all connected. I also already asked my supervisor to put in a good word for me a few weeks ago and she said no worries, so I don't want to be too much.
I do REALLY want this job, so I don't want to appear desperate or inappropriate.
What would be the right thing to do here?