Here's a friendly suggestion to do things differently ....
Especially when traveling with young kids near bedtime, the last thing I want to do is trust the airlines with all of my necessities. Because of this, no matter where I fly, I always pack for our first 24 hours' needs in our carry-ons (you're allowed one carry-on per ticketed passenger) just in case the AIRLINE delays our luggage.
And because I pack this way, I really have no care when my DME luggage is delivered to me. In fact, when I arrive late, I request that my DME bags be held 'til the next morning so we don't get awakened in the middle of the night.
The last thing I'd want to do is find that the airline delayed one of my bags and I don't have everything I need for my toddler for bedtime and the next morning.
Stopping and waiting at baggage claim will likely delay your arrival at your resort. In the time you're detouring towards baggage claim and waiting there, and then dragging your bags to the DME area, it's quite likely that the bus you COULD have been on has already left for your resort, and you'll have to wait for the next one. To me, with a little one, my top priority is getting that little one to bed ASAP, and if Disney gives me a way to do that (skipping baggage claim) then I'm going to take them up on their offer!
So there it is ... my recommendation for letting DME handle your luggage for you, and calling for it the next morning.
But PLEASE, even if you plan to claim your own luggage, PLEASE pack your carry-ons like I suggested, anyway, just in case the AIRLINE delays your bags.
Have fun!!!