You'd say "She is a teacher". You could say "Her job is to teach", but that could refer to any job that requires teaching. You could also say "Her job is to be a teacher", but that doesn't sound nearly as natural as "She is a teacher".

You can't say "Her job is a teacher" is because a teacher is a person who does teaching work. She is a teacher, not her job. In that sentence, you would have to use an adjective to describe "her job." In this case the adjective would be teaching, So the correct sentence is "Her job is teaching." However It would be best to avoid using "her job" as the subject of the sentence. You should better say: She is a teacher or she work as a teacher.

She is a teacher. She works as a teacher. Her job is teaching/to teach. These are the correct forms.

It is more natural to say "She is a teacher." We already know that teaching is a job so you do not need to say it.