Hi there Palestrina!
Thanks for bringing your wonderful question to the Disney Parks Moms Panel. I can't tell you how happy it makes me to see families take little babies to the Disneyland Resort. You will find that
Disneyland Park and
Disney California Adventure Park are very accommodating to families and children of all ages. As you may be aware, your two month old baby can ride with you on any attraction that has no height requirement. We took our son as an infant and really had so much fun on many more attractions than we expected.
Personally we did not find the noise on most attractions to be too loud, but I will say that we brought noise cancelling headphones with us and did not regret it. During some of the louder nighttime spectaculars or fireworks we had our son wear these headphones. Also he wore them when he was napping throughout the day in a loud environment or if we took him on an attraction when asleep. It definitely wouldn't hurt to take them with you in your bag and have them handy when you get on an attraction just in case! It is one of the items I always tell families with babies to bring, because you really never know when they may come in handy.
I want you also to be aware of the very convenient
Baby Care Centers located in each park. They are great places to change, feed, or just get a little privacy with your little one. You can also purchase any infant necessities here that you may have forgotten. I even love just seeing some of the beautiful art hung on the walls at the Baby Care Center in Disney California Adventure Park!
I can't wait for your magical vacation, and feel free to return if you have any other questions!
-Jennifer