A 28-year-old woman with type 1 diabetes mellitus presents to the emergency department with severe nausea, vomiting, and rapid shallow breathing. Arterial blood gas shows pH 7.18, HCO₃⁻ 12 mEq/L, and PaCO₂ 28 mmHg. Serum glucose is 450 mg/dL, and serum ketones are markedly elevated. She admits to missing insulin injections for 3 days. What is the most appropriate immediate next step in management?