I think it is wise to have a notarized note, just in case. It's hard to know what you will run up against. Here's two stories with opposite situations.

1) When my husband, 6 year old son, and I went to Australia, we flew out the airport in Sydney. I wanted to shop a little longer and use up currency in the airport shops but my husband was getting restless. I said, "Go on ahead into the waiting area. Yossi and I will shop a little longer then join you." When I finished shopping, my son and I went over to the entrance to the waiting area. At that point, I had to talk to an immigration official. He said "You can't go through here without the boy's father?" I pointed out that he had gone ahead. They had someone go get my husband and bring him back. I wasn't allowed to leave Australia with a child without either the other parent or paperwork.

2) I traveled to Japan in 2007 with my husband, my son, and my nephew (my sister's son). I made sure to get notarized paperwork stating that it was ok to take my nephew out of the country and that I could make decisions for his healthcare. Not a single person ever asked for it. Even though the kid had a different last name from all of us on his passport. My guess is that lots of families have different last names and since this child was older than mine and looked enough like me, they thought he must be mine from a previous marriage. In any case, I had paperwork but never needed it.

So, based on those examples, I think I would rather have the second situation where I could feel secure than go through something akin to the first.

Thank you Kathryn! I appreciate your feedback. Our family usually always travels together so I have never run into this before! I will get a note to be sure we are good!
THANKS!
Katie

Since it's your first time to travel alone with your child, I also suggest to get a permission letter allowing you to travel to avoid problem at the immigration. (just in case)