G6PD Deficiency is an inherited condition, and so one cannot get it by infection or contact with someone who has G6PD Deficiency.
As the above condition is genetically inherited, these are the possibilities for how your daughter may have inherited it:
A) If the father is unaffected (healthy) and the mother is a carrier (no clinical symptoms):
One daughter out of two will be a carrier
One son out of two will be G6PD deficient
B) If the father is G6PD deficient and the mother is unaffected:
All daughters will be carriers
All sons will be unaffected
C) If the father is G6PD deficient and the mother is a carrier:
One daughter out of two will be G6PD deficient
One daughter out of two will be a carrier
One son out of two will be G6PD deficient
One son out of two will be unaffected
D) If the father is unaffected and the mother is G6PD deficient:
All daughters will be carriers
All sons will be G6PD deficient
E) If both father and mother are G6PD deficient:
All daughters will be G6PD deficient
All sons will be G6PD deficient
Also, with regards to the Newborn screening test being normal, the test may have been done too early or the blood sample taken was too small to diagnose the condition.