Good point. The question would be if the gut microbes were fully populated.
Babies are definitely out. But a 2yr old should just be entering the good zone, and will only get better over the year. I think a lot of development occurs by 3 months:
www.medicinabiointegrata.com/doc/probiotici/Microflora%20intestinale%20nel%20bambino.pdf... but I can't readily find a guideline for completing development.
I understand members of the same household are discouraged, but I think this applies mostly to closely related adults.
I do read that the mother's microbiome diversity, manner of delivery, and even breast/bottle feeding can change the timing of a child's gut microbe development.
Maybe it would be best to wait another 6-8 months.