Children that are raised on farms and have regular exposure to livestock in their first years - on average - grow up to have few if any allergies as teenagers and adults. There was a vid or article (posted here?) a couple months ago discussing this.

Get out in the fucking dirt.

If you try to live in a sterile bubble, it's a bit like having an amp with a floating input, it'll pick up stray signals and massively amplify them. In the immune system, this manifests as auto-immune diseases (from allergies through to horrific disorders which cause massive pain and eventual death).

Your immune system requires input, a wide variety of input, to develop a robust response. The process is hormetic, in that limited exposure over time will strengthen your immune system (granted that you are adequately nourished, e.g. you have sufficient Vitamin D levels, etc). I wouldn't limit it to just dogs, or argue that dogs have some special benefit over other sources of immune stimulus. Soil bacteria, and particularly strains like Mycobacterium vaccae are very important to the immune system and can even be used as an actually legit "vaccine", in that it can reset the body's immune system.