A 28-year-old woman with type 1 diabetes mellitus presents to the emergency department with severe nausea, vomiting, and rapid breathing. Blood glucose is 450 mg/dL, arterial pH is 7.18, HCO₃⁻ is 12 mEq/L, and serum ketones are markedly elevated. She admits to missing insulin injections for 2 days. What is the most appropriate immediate next step in management?