Also to add, not only does it need a new square but from my experience of saving a slot till agriculture was researched it still was not enough, it needs to be a hamlet.
In my last game I built a farm immediately after founding a city and it worked ok for me:

It looks like there should be enough plots for the farm there (2 map tiles/8 miniplots in addition to the base city and only 2 miniplots used by the looks of it). I'd be willing to call it a bug unless, as you said, they meant for you to only have one farm (which is odd imho).
I had filled 2 plots (with about 6 miniplots) previously before canceling builds. Apparently canceling things doesn't free up plots. Now that does sound like a bug ...