We have 17 months old daughter. We stopped hosting for the first year as we can offer only shared room and I was concerned about her sleeping more than anything, I wouldn´t want my guests not to get good night sleep because of her cry. Since she started sleeping all the way through the night we started hosting again.
I think it is very important for the guests to know that there is going to be an infant or a toddler in the household. I understand that some people are not very much into children or when they are on their holiday they want to maybe escape their own little ones 🙂
So honesty is the most important thing. The next is to be confident that your little one will be comfortable with strangers. The best is to observe this at the playground or in the park. Does he/she get scared when someone strange is around? Ask your friends that he doesn´t know so well to test him. You wouldn´t want to stress your child when hosting so if he/she is not fine wit strangers I wouldn´t push it.
From my experience I have to say that all of our guests were so kind and friendly wit our daughter that she is always looking forward to meet the next guests. She comes to the door and gives huggs when new people arrive, she shows her toys and wants to share with her snack. I think this is absolutely amazing ang I am glad Airbnb provided this opportunity for her to meet people from all over the world, realize that we are all the same human beings.
As to the question about the safety of the child. Obviuosly our little one is too young to be left alone so there is always someone with her or around. I pay attention to the hosts profiles and try to communicate with them as much as possible before their arrival.
From our positive experience I would recommend hosting with child as long as your child is fine with strangers.