A 3-year-old child presents to the Emergency Department with a 12-hour history of high fever (39.8°C), lethargy, and vomiting. On examination, you note a widespread non-blanching petechial rash predominantly on the limbs and trunk. Vital signs are: HR 170 bpm, RR 45/min, CRT 3-4 seconds, BP 80/45 mmHg. The child appears peripherally shut down. What is the single most important immediate management step?