It is possible to sometimes become immune to dog allergies and outgrow dog allergies later on in life.
Sometimes being exposed to a dog that you suffer allergies from can help you become immune to the dog allergies and then you may be able to keep the dog.
However there's no guarantee that you will outgrow the dog allergies and you may continue to suffer from the dog allergies for the rest of your life.
The hair and dander as well as the skin particles is what most people are actually allergic too so by bathing your dog often enough and brushing them to keep the dander and skin flakes down you can sometimes live with a dog even when you're allergic to them.
If you're still allergic to the dog after 6 months to a year then you're unlikely to outgrow the dog allergies.