A 5-year-old girl is brought to a community health clinic by her caregiver due to a generalized rash that appeared approximately 48 hours prior. The rash was initially noted on her face, described as a fine, pink maculopapular eruption, and has since progressed caudally to her trunk and extremities. Her medical history is largely unremarkable, and she is up-to-date on routine childhood immunizations, though her specific vaccine records are not immediately available. On examination, her vital signs are: temperature 37.8°C, heart rate 95 beats/min, respiratory rate 18 breaths/min, and blood pressure 98/62 mmHg. Oxygen saturation is 98% on room air. She appears comfortable and is playful. Physical assessment reveals diffuse, non-confluent, blanching pink macules and papules, predominantly on the trunk, with some fading on the face. Notably, there is mild bilateral conjunctival injection and tender posterior auricular and suboccipital lymphadenopathy. The rest of the examination is unremarkable. Given these findings, what is the most appropriate initial management strategy, and what public health measure should be considered?