How many doctors are there? Very good work!
You had
4 big problems:
1. How many or How much? You haven't learned this yet, but you got it anyway. Doctors are things that can be counted. So we say How many.
2. Then you had to decide whether to use doctor or doctors. How many told you the sentence was guessing there was more than one. Also, you didn't have an article to make a doctor.
3. You saw that you needed to put doctors after How many. This is difficult, because if you were asking for an indefinite number of doctors you would say "Are there many doctors?"
4. Is there or Are there? If the correct words had been How much then you would have use Is there. But you wouldn't say "How much doctors" so you knew it would be How many and that meant you needed are there?