Of course she can bring her child with her as a single mom, provided she has sole custody or permission from the father (if he is still legally involved with the child at all).

She should, of course, bring all relevant paperwork with her -- marriage or divorce certificate (if she was married to begin with), child's birth certificate, letter giving permission from father for her to travel with child outside of the country OR court document stating that she has sole custody, etc.

If your friend wasn't married to begin with, then it is still not an issue to enter with her child. It may become an issue if/when she goes to apply for a visa for a nanny to watch her child while she's at work, because for this they ask for your marriage or divorce certificate.
Not sure what they would do if you didn't have either one...but it must have happened at some point, and if not, then they'll need to have a procedure in place to handle it soon because it's not all that uncommon to be a single, unwed mother.

There are many single moms here with their children, working and taking care of their families. Your friend should be no different.