This study isn't all that convincing.
First, the sample is too small.
Second, the study isn't conducted in a controlled environment either. They simply picked a few hundreds infants and did surveys with their parents.
Even if the finding is true for a much larger sample, there still could be other explanations. If you have read the reader comments, I see a few possible other causes for the study results. One of the comments said it is possible when there are pets around, the parents pay closer attention to the babies. Often time the mother is presence and the breastfeeding gives better immune system to the baby.
Another comment said it is possible the exposure to the micro-organisms on the pets made babies' immune systems stronger.
I do not know for sure, but until there is a study conducted on at least 10x larger sample in a controlled environment, I am not convinced. Sorry.
