What's the big deal? If you're comfortable feeding a 3mo in public, then why not a 1yo? Between about 4m and 1y I tended to use Mother-and-Baby rooms, or somewhere discreet to feed dd, but that was because during that period she was an awful thrasher and I disliked having my breast periodically displayed to the world. Dd was still having daytime feeds at 18m and I happily fed her in public - in fact, at that age I prefered not to feed in MaB rooms because I felt that I might be rubbing it into the faces of mums who regretted having weaned.
I can't understand why it should be an issue, but so many mums have said that they fed to a fairly advanced age 'but only at home'.