If you were born and brought up in the US, then the baby is a US citizen as from birth, I think. The registration and passport are mere confirmations of that status, she does not have to be "naturalised" first.
This is the specific requirement in the citizenship statute
The following persons shall be US citizens from the time of their birth:
...
"a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years:"
So you should have been physically present, as a US citizen, in the US for at least 5 years in total prior to the birth of the child, at least two of which have to have been after the age of fourteen.