I am trying to file a 1099-Misc for a nonprofit that I am treasurer for. It is not my income, but I am trying to report it. Is this possible on TurboTax?

Not really.  You would need Turbotax for Business, which you don;t need for anything else since I don't think it files form 990.

There are several web sites that will e-file a single 1099-MISC for around $5.  I probably should not use this forum to mention a specific competitor, but I used such a site when I needed to issue a single 1099-MISC as my church treasurer.  It worked fine.