If u have to pay for the publishing they are not 'real publishers' they are what is called Vanity Publishers as mentioned above.
I am sure your daughter is good.., all u can do is possibly find some online publishing sites on the web.., that can be a route in but make sure u have dated copies of any work u put on the web in case of plagerising.
Otherwise its a case of using google to find children's publishers (assuming she is writing children's stories) and sending copies of the stories to all of them in the hope that they will reply with a yes or no.., and possibly some advice. Remember the first page has to be a 'tag and hold' front page as a lot of publishers won't even get past the first page. It can also be good to send stories to agents.
Be prepared for 100's of no's..,but remember that u only need one to say yes.
However, having said all this.., it might be best to wait a while before launching her into the world of publishing unless u think she has written a particularly good story or collection of stories. There are legal problems with any child author.
Good luck.