That is classic presentation for leukemia. The differential on the elevated WBC tends to lead us to a more definitive diagnosis. Bone marrow aspirate examination is usually recommended to confirm diagnosis.
The basic rule outs are overwhelming infection or leukemia and the blood tests normally point us in the correct direction.
Going to a specialist is recommended as the access and administration of chemo agents are usually beyond many practices.
I've had many patients over the years, most owners elect euthanasia when they get to "that point." But, I've had several get into remission with chemo and have a year plus of quality time.