It is an eTicket, so you'll simply need to show up at the airport to get your boarding pass. Very rarely are paper tickets issued, anymore. Even if you don't have your info, the Delta check-in kiosks at the airport will allow you to type in your name and destination, or (as I do) swipe a credit card (any card) to get the name info from it.
Now to derail the topic a bit, with Delta you will want to watch your seats like a hawk. No stress, just vigilance. This is because Delta tends to do a lot of aircraft swapping, and the computer system reassigns everyone. As such, you'll need to watch your seats to be sure your party remains together.
As mentioned, get the confirmation number from Disney Travel. Then, go to Delta's website, click on My Trips and enter the info requested. You will be able to choose your seats, in case you want to try and get closer to the front or sit in a certain row. Then periodically (usually I check twice per month until 30 days out, then weekly til one week out, then daily) check to be sure your seat assignments are the same. If not, just reassign them yourself online.
Sometimes we get mad at this, but the system is working as intended, which is to reassign seats during travel instead of pre-travel, to be sure everyone gets to their destination on time. In essence, no worries. if you have a concern, call Delta. Their agents provide good customer service. If you would like to understand what is going on, just post on here and we can provide insight and tips.
One last thing, normally I would suggest opening a SkyMiles account, but Delta has a recent policy to limit the amount of frequent flier rewards from third party (
travel agency) booking, since the agencies receive a commission (another good reason to book directly with the airline). However, you can open a SkyMiles account and add your confirmation to make the period checking easier.
Good luck and have fun!