I feel like the causality is likely backwards from the title - if you are less vulnerable to disease, you can better afford to boldly take risks and explore new situations and withstand the possible negative consequences.
That would presuppose that the dog knows that he has a fit immune system, which we couldn't really explain either. I think the causality relationship is less interesting than that there's a correlation between different aspects of interaction with the environment. Maybe the causality works both ways even?
So this is the research area that I currently work in, albeit with a disease ecology perspective rather than a biochemistry one. I've had a quick read of it and and although it does seem to track other research that has been done ("Why are behavioral and immune traits linked?" by Lopes 2017 is a nice review) I'd love to see some power analyses - the sample size seems pretty small for something as complex as this question. The study I'm helping with now has a minimum sample size in the hundreds, for instance, for a broadly similar question. PCA-ing a few tests together is pretty common, but also comes with a lot of potential biases (see "Avoiding the misuse of BLUP in behavioural ecology" by Houslay and Wilson if anyone is interested!)
