This study is being done to study how exenatide, an FDA-approved drug that lowers blood sugar in non-pregnant patients with type II diabetes, works in pregnant women. To do this, the investigators will study the drug's pharmacokinetics (what the body does to the drug; specifically, how quickly your body breaks down and excretes exenatide) and pharmacodynamics (what the drug does to the body; specifically, how effectively exenatide helps the participants' pancreas secrete insulin and how well it controls blood sugar after a meal). There are only two main drug therapies (insulin injections and glyburide pills) currently used for gestational diabetes and not all women achieve good enough blood sugar control without side effects. Therefore, the investigators hope to find out if exenatide might also be helpful in gestational diabetes.