I am glad your vet isn't at this as a typical "allergy" and I am interested as to their perspective and how to treat. Any suggestions?
I would think at 4.5 months old it would be speculative about genetics being "the cause". I would lean towards vaccines and deworming as cause for this deficiency...thus causing immune malfunction which is dubbed in most conventional assessments as "allergy".
When I first read this I immediately thought of Jax thread awhile back. Very informative.
Look into Bovine Colostrum - Proper Nutrition makes one that is 40% immunoglobulin as suggested in Dogs naturally (will find link)
However read this
Immunoglobulins (A, D, E, G and M) – the most abundant of the immune factors found in colostrum; IgG neutralizes toxins and microbes in the lymph and circulatory system; IgM destroys bacteria while IgE and IgD are highly antiviral (4,23,25).
Other immune Factors
– some of the documented immune factors include secretory IgA, IgA Specific Helper, B Lactoglobulin, Lactalbumin, Albumin, Prealbumin, Alpha 1-Antitripsin, Alpha 1-Fetoprotein, Alpha 2 macroglobulin, Alpha 2-AP Glycoprotein, C3, C4 and Orosomucoids
found here: Colostrum Article in the American Journal of Natural Medicine | SynertekColostrum.com
And Dogs Naturally article