Hello Jennifer! Welcome to the Disney Parks Moms Panel.
On our first Walt Disney World Resort vacation as a family, we also stayed in a
Little Mermaid Suite at Disney's Art of Animation Resort.
You are thoughtful to consider the comfort of other guests when it comes to your little Mouseketeer. When we visited, my son had a hacking cough and we were worried about how that might distract others at night. We
requested a corner room through Online Resort Check-In and a
crib for our little one's comfort. While Cast Members cannot guarantee to grant a room request, it never hurts to ask (especially when considering those around you).
We never noticed ambient room noise from others nor did we ever receive any feedback about our son's coughing. When we visit, I download a white noise app for my smartphone to block out any noise from kids running down halls or pool music during nap time. While that doesn't solve the issue of noise you create, you may find it useful for creating an environment suitable for your 6-week old.
If you are concerned,
The Family Suites at Disney's Art of Animation are larger and quieter. We opted to relocate to a Family Suite during our trip, not due to the noise from others, but my son's hacking cough was keeping the entire family from getting to sleep and the extra room was helpful.
I recommend that you mention your concerns with the Front Desk when you Check-In as they will do all they can to find a room that best suits the needs of your family and the Guests around you.
Have a Magical Vacation!
~Todd