Absolutely. You are welcome to bring a backpack, purse, or diaper bag
with you into the WDW parks. When I'm at WDW I rarely travel light. As
a matter of course, I have with me at least one camera (often two or
three), a hat, sunglasses, sunscreen, a few bottles of water, a poncho
or umbrella, a sweater (I get cold in air conditioning), a cell phone,
my wallet, snacks for the kiddos, a basic first aid kit, etc. Most
often I carry all this with me in a backpack.
You should know that there is a security checkpoint as you enter the
parks. You will be required to open your bag for inspection. There is
no need for concern about this, all the items I've mentioned above are
perfectly fine to bring with you.
For the answers to other commonly asked questions about Disney theme park visits, you can click
HERE.
Have a great trip!