No, the first one is correct.
Here you are asking a question, so by adding 'is' after 'she' renders the second one grammatically incorrect. It's almost as if you are answering your own question with the second one because 'she's running to school' implies an affirmative answer to the question. The only other thing is if you are asking whether she runs to school on a regular/general basis, then it becomes 'does she RUN to school?' not 'running'. However if you are talking about the present and that specific moment, then it becomes 'IS she running to school?'
'Does she run to school?' - in general
'Is she running to school?' - right now.
'Yes/(no) she does /(does not).' answer to first question.
'Yes/(no) she is/(not).' Answer to second question.
I hope that makes sense...?