Depending on what time of year you go, you can get reservations on the same day! It's awesome! I've called the morning of several times and been able to score Cafe Orleans, Big Thunder Ranch BBQ, Carnation Cafe and others. So it is certainly not as intense as WDW. You can't always just walk in, but usually you can call a couple of hours in advance and get a reservation, unless you are there at the busiest times of the year.
Now the caveat is that I would totally make reservations in advance for any of the character meals and some of the more popular restaurants if they are on your "must do" list. Those are pretty much just Carthay Circle and Blue Bayou though, and of course the character meals. And even those don't fill up too fast. I'm going in three weeks, and I had to call yesterday to change my Carthay Circle reservation. They had plenty of open times! So even a week or two before is probably fine.
I know this probably sounds crazy to WDW vets, but it's true! I am totally a 160 days out, first thing in the morning reservation booker at WDW, but it's just more relaxed at DLR. Which I'm sure you'll notice in other areas as well! It's just a more easygoing trip, because it is so much easier to get around and see what you want to.
Hope you have a great time!