Can I issue IDP payments for a child if she has a certificate...

Of course you can. The main thing is that your circumstances meet the requirements for granting IDP status. And this is in accordance with Article 4 of the Law "On Ensuring the Rights and Freedoms of Internally Displaced Persons": the basis for taking into account an internally displaced person is living in a territory where there is an armed conflict, temporary occupation, widespread manifestations of violence, violations of human rights and natural emergencies or man-made.