You should not be able to play confidently without a teacher until you have three skills at hand: inner discipline, good technique, and one’s own style. All three of these skills apply to ALL genres of music—be it classical, jazz, gospel, or honky-tonk. Let’s take each skill separately.
First, having inner discipline compels a pianist to practice without a teacher’s encouragement or admonishment even when the desire wanes. Inner discipline is what drives a pianist to practice efficiently as well. For example, a pianist who is disciplined can learn more during an hour-long practice session than a pianist without discipline can learn in two hours. The former pianist has more focus and attention than the latter. Also, a good pianist would practice a piece only a few measures at a time rather than simply “getting the gist” of a work.
Secondly, a teacher-less pianist must already have good technique. Such a pianist will concentrate on fingering, clarity, pedaling, posture, hand position, rhythm, tempo (possibly with the assistance of a metronome), etc. Having a good ear is critical to your technique. A pianist without a teacher must be able to hear errors and be able to correct them.
ONE’S OWN STYLE
Lastly, a pianist who chooses to go solo must already have a sense of his/her style. The mark of a good pianist is the musicality of the music the pianist plays. This may sound redundant, but I am sure you can imagine the difference between a song played by an amateur and the same being played by a professional. Even when the same exact notes and rhythm are played by both, the professional version would simply sound better.
A teacher imposes his/her own interpretation of a work—how s/he hears or feels the melody. Without a teacher, a pianist must be able to develop his or her own sense of the music. For example, different pianists may imagine color, or images; they may create stories or simply feel emotions to make the music they are playing come alive. Accordingly, different pianists would voice or phrase the same work in dissimilar ways.
As for you, without having one of these three skills, you would need a teacher for guidance. How long it takes for you to feel confident to cut your teacher loose depends entirely on you, your skill set, and your desire. For most people, being a musician is a lifelong journey, which entails lifelong learning. There will always be someone who can teach you something.
Are you really ready to be a pianist without a teacher? Odds are, probably not ;-)