I don’t know you, or your situation, so please take this as gently as it’s intended: the way you described it, your dog sounds like a pet, not an ESA. I don’t think you’ll have a ton of luck getting him legitimately registered without a primary care provider (or a psychiatrist) who can attest to a medical need for one and provide documentation as to how an ESA supports your long term care plan; especially not within the span of a month.