I'm aiming for the same goal for my existing startup. Except in 3 months and the app (https://carelogger.com) has been running for a few years (almost entirely part time or while I was employed).
My app had been free for the majority and an earlier attempt to make it profitable was half-hearted, before we made it free again.
Now, we have a B2B version, a large email marketing list, and multiple native mobile apps coming out next month. We hope these will push it to profitably ($4-5k/month) by then.