A person can’t build up an immunity from uncontrolled casual exposure. If that were true, allergies wouldn’t be a problem. However it is possible for some to do it gradually and in precise steps through a lengthy series of allergy shots. Growing out of an allergy is unlikely, but sensitivity with age can change, and more likely a person learns to avoid or limit exposure as they grow older.
I am not a medical professional, just a guy who has been around for a while, raised on a farm and seen plenty of allergies. Also had them myself...
Some you outgrow, some you don't (like hayfever)
This allergy to a dog lick, is probably due to a enzyme in the spit that the child had never come into contact with before and will most certainly contact in the future...But not being there I can't say for sure..It takes some work to determine it.
But as long as the allergy is not serious and contact with the animal can be controlled. In my opinion it is better to try to condition the child to the allergen or substance because going through life with a pet allergy is not going to be pleasant for the kid, or for future acquaintances and friends.
That's all I have to offer....based on my own experiences. Many kids today, and even a couple of my grand kids, have been too removed and protected from various substances, bacteria and other things in a effort to protect them, and the ability to do this because of the changes in society over the decades....(like sanitary daycare) and so forth. As a result when to contact these things, they can react severely. Develop issues where you feel the need to protect them. But what if the protection is actually making it worse. Or in some cases, causing the reactions.. Life is a dirty place. Kids will get into it and you cannot stop that. If there is even a slight possibility that you can condition a child to live in that dirt without a reaction, I think it's better to do that rather than try to eliminate that dirt from his path in life. That's my opinion.