I think the very best way to determine if a teacher is the right one is first to ensure the child enjoyed the very first lesson and that there is some rapport and understanding between the student and child.
The next thing to check, after a month or two, is if the child is practising. If you can see practice occurring and the child is happy to discuss his or her progress or what took place in the lesson, this would be a good sign.
However, more important than either of these is: How is the child progressing after a year? Can you see a difference in the playing? Is the child enthusiastic about his progress? Are you proud of what your child has achieved? If so, stick with the teacher.
Not all students are perfect for all teachers and not all teachers are perfect for all students, no matter what their qualifications. It really is a bit of a hit and miss affair to begin with, although finding a teacher through recommendation is probably the best route.