Viral or Bacterial Infection: The presentation of fever, elevated white blood cell count (WBC) of 15, and neutrophilia (neutrophils absolute 11.2, neutro auto 74.8) in an 18-month-old child is most suggestive of an acute infection. The high percentage of neutrophils (74.8%) and the absolute neutrophil count indicate a likely bacterial infection, although viral infections can also present with neutrophilia, especially in young children.

Urinary Tract Infection (UTI): Given the age and symptoms, a UTI is a plausible diagnosis, especially if the child is not yet toilet-trained and thus more susceptible to such infections. The elevated WBC and neutrophilia support this possibility.
Pneumonia: Respiratory infections, such as pneumonia, can present with fever, elevated WBC, and neutrophilia. Clinical signs like cough, difficulty breathing, or chest retractions would support this diagnosis.
Gastroenteritis: Although often associated with lymphocytosis, bacterial gastroenteritis can cause neutrophilia. Symptoms such as diarrhea, vomiting, and abdominal pain would be indicative of this condition.

Meningitis: Although less common, bacterial meningitis is a critical diagnosis that must not be missed due to its high morbidity and mortality. Symptoms can be non-specific in young children but may include fever, irritability, and signs of increased intracranial pressure.
Sepsis: The combination of fever, elevated WBC, and neutrophilia could indicate sepsis, a life-threatening condition that requires immediate intervention. Clinical signs of sepsis include systemic signs of infection plus organ dysfunction.
Osteomyelitis or Septic Arthritis: These conditions, although less common, can present with fever and elevated inflammatory markers. Local signs of infection, such as swelling, redness, or decreased mobility of a limb, would suggest these diagnoses.

Leukemia: Although rare, leukemia can present with elevated WBC counts. However, the differential count would typically show blast cells or an abnormal distribution of cell types, not just neutrophilia.
Juvenile Idiopathic Arthritis (JIA): Systemic JIA can present with fever and elevated inflammatory markers, including WBC. However, other systemic symptoms and joint involvement would typically be present.
Kawasaki Disease: This condition can cause fever, elevated WBC, and other systemic signs. Specific criteria, including rash, conjunctivitis, and changes to the lips and oral cavity, are required for diagnosis.