Here's a link that will explain Cushings:

Cushings

Not all symptoms have to be present, and the Dexamethasone, ACTH suppression tests should provide a diagnosis. If left untreated it will readily damage the kidneys.

Given the array of symptoms you are seeing which are consistent with Cushings you should get the dog tested. If your current Vet resists, then ask for a referral to a specialist in order to get a diagnosis.

Prolonged treatment with Prednisone (e.g. just a few months) can induce Iatrogenic Cushing's. Yet another reason not to over use Prednisone for simple things such as allergies. For things like autoimmune diseases it's used to help get things under control, before switching to a Chemo drug such as Cytoxin, or Methotrexate.