setting up first child domain

My company has recently merged with another company. Therefore I’m setting up a child domain to our parent domain. I would like to know a few things about setting up a child domain. First of all I would like to know about dns servers. Does the child domain use the dns servers of the parent domain or should I set up its own dns server? I assumed it had to use the dns servers of the parent domain because when I went to create an account in active directory. I recieved an error that there was know global catalog server to verify the uniqueness of the username, but when I entered the parent domains dns servers in I did not recieve this error.