For a first camera...the G7 may be a little too much.

The G7 is a premium camera aimed at the advanced photographer.
To get your money's worth, you really should take a photography class first.

A less expensive version of the G7 is the Canon A710IS.
About $200 less.
I don't know if it has face detection.

The F31fd is the updated version of the F30.
I am not sure that it is in the stores yet.

There are no reviews of the F31fd, but I would expect it to perform as well as the F30. It should do well for a family with a new baby.
It does not have optical image stabilization, but with a 3X zoom you really don't need it.