Pharmacology of Exenatide in Pediatric Sepsis, PEPS is a phase 1-2 investigation that will examine safety, pharmacokinetics, pharmacodynamics, and preliminary clinical efficacy of 4 subcutaneous doses of exenatide administered every 12 hours to children with newly diagnosed septic shock. The investigators' long term goal is to explore the potential benefit of exenatide on: early immunomodulation and glucose homeostasis, organ dysfunction, and clinically meaningful outcomes associated with pediatric sepsis. The current study objectives are to conduct a "3+3" dose escalation study, and then examine a "best exenatide allometric dose" to generate safety, pharmacokinetic, pharmacodynamic, and initial efficacy data in a larger cohort. In Phase 1 (three allometric doses; three age strata)the investigators will identify an exenatide dosing regimen that mimics area under the exenatide concentration curve for exenatide dosing among adolescents with type 2 diabetes with minimal or no adverse events. A total of 18 subjects are expected to be enrolled in Phase 1. In Phase 2 the investigators will utilize this "best exenatide allometric dose" to further clarify exenatide safety (adverse event occurence: e.g. nausea, abdominal pain, delayed gastric emptying, hypoglycemia, pancreatitis, renal dysfunction), pharmacokinetics, pharmacodynamics (glucose homeostasis; inflammatory cytokine serum concentrations), and effect on clinical outcomes (AUC of Saturation Index, AUC Vasoactive-Inotropic Score, AUC RIFLE Criteria, Pediatric Logistic Organ Dysfunction Score; changes in health-related quality of life and functional status). In Phase 2, 30 subjects in each age strata in the ratio of 4:1, exenatide: vehicle, are expected to be enrolled.