Can we use the HIV antibody test to detect HIV in newborns?
The rapid screen usually tests the oral mucosa by swabing the inside of the cheek and checking for the presence of anti-HIV envelope antibodies. Although the precise target of these antibodies seems to be kept propriatary, my guess would be the detection of either p24 antibodies or envelope antibodies that bind the V3 region. 

Regardless, the point is they test for the presence of antibodies, which a child does not start making until they are born. See this post for a great explanation 

Since a child has mostly maternal antibodies, the presence of anti-HIV antibodies would only mean that the mother has started producing antibodies to HIV (Seroconversion). This means that although the child has been exposed, they may themselves not be infected. 

The mucosa, particularly in the oral region has a very low titer of anti-HIV antibodies, so I think this test would probably be best to direct the physician to conduct additional tests that are more indicative of HIV infection like p24 western blot.