Hi Mandi,
This is such a great question that I think a lot of Guests have. We have been taking our kids to the Disneyland Resort since they were just a couple months old, so I understand the importance for a nap. A lot of the attractions cannot accommodate strollers, so the strollers will be left outside the attraction. I have found from personal experience that if you can use a baby-wearing device for your daughters naps you will be able to enjoy more attractions. I used to put my little one in a baby-wearing device then head to some of the longer attractions like "it's a small world", the Disneyland Railroad, or the Pirates of the Caribbean that way I could enjoy the attractions while my child naps.
Another option you could try is to head over to Disney California Adventure Park into the Animation Academy. Whether it's for a nap, a mama break, or to let the kids get their wiggles out, I think you will find this to be a magical rest stop. It's not exactly quiet but it's a huge room with large screens playing memorable clips from your favorite Disney movies and songs to go along. There's more rooms to explore in this building too.
You also can head to the
Baby Care Centers at either Disneyland Resort park and use their facilities during regular park hours. I utilized this facility for both of my kids for nursing. They have comfortable rocking chairs so if you wanted to relax or rock your daughter to sleep this is always an option.
I hope this helps and that you all have a pixie-dusted trip. If you have any more questions please write me back.
I hope you are having a Practically Perfect Day!
~ Lynette