Could unstable blood sugars be the cause of undiagnosed constant nausea for 1yr?

Not sure...: What you mean by "unstable" blood sugars. Blood sugars normally fluctuate through the day with eating, activity, etc, so noone sits at just one level. Infants and toddlers can generally tolerate slightly lower levels than adults. What symptoms is baby/toddler showing that you know he or she has "constant nausea" - i would focus more on the behaviors than on asuming its nausea.

Unstable blood sugar: If your blood sugars are high then yes nausea can be a result. Uncontrolled diabetes can be a cause of a many signs and symptoms of poor health: fatigue, weakness, weight loss, vision problems numbness of your feet and others. Find out what your glycated hemoglobin is. (a blood test).

Blood Sugar : Yes. If you are an undiagnosed diabetic, or there is another cause of vacillating blood sugars, hyperglycemic episodes are frequently associated with nausea, especially if there is a build up of ketones in your system, , a common consequence of high blood sugars. Of course, you will want to follow up very soon with your doctor and get tested.