Pneumonia is a diagnosis made by auscultation of the chest by your paediatrician and supported by a X-ray. Blood counts,if raised with higher neutrophil count also indicates bacterial infection. Hospitalization is required only in 2 conditions,one,if child is very serious and second,if child is very dull and not eating at all. If you think she's active and eating normally,AND you see clinical improvement in terms of reduced fever and better oral intake,no newsboy hospitalize.