Is performing the Kesh-Mundan of a 13 months old girl child in accordance with the Hindu religion and scriptures? We follow the south Indian traditions from Karnataka.
Here is what R.B. Pandey says in this excerpt from his paper "The Hindu Sacraments (Samskaras)":
Chudakarana (tonsure) is the eighth samskara[.]... According to the Grihya Sutras, the chudakarana ceremony should take place at the end of the first year or before the expiry of the third year, though later authorities extend the age to the seventh year.
Now different sutras may say different things on the subject, so it depends on which sutra is followed your family tradition. For instance, I'm a Yajur Veda Brahmana (meaning my family helped preserve theYajur Veda), and my family specifically follows the Apastambha Sutra (a Sutra associated with the Krishna Yajur Veda), which says this:
In the third year after his birth the Kaula (or tonsure is performed) under (the Nakshatra of) the two Punarvasus.
So you might want to find out similar information concerning your family traditions in order to carry things out properly. You can consult a family priest if you have one.