The Life and Lies of Albus Percival Wulfric Brian Dumbledore

Neville wouldn’t be part of the quest.
Dumbledore is meticulous about the setup here. All the tasks are designed to be passed through by the whole trio. . . until the last one before the Mirror, Snape’s potion puzzle. Here, there is a potion to move backwards as well as forwards—what is the need of this, if not to send Ron and Hermione back to safety? And as for the potion to move on to the next room: “There’s only enough for one of us” (SS286). Yet there’s no mention of there being not enough potion for more than one person to go back. The intention is clear: only Harry is to move on and face Quirrell, while Hermione and Ron are to go back.
Why is this? Because Ron and Hermione, unlike Harry, have no magical protection from Quirrellmort. And Dumbledore does care about students’ safety, to some extent. So he doesn’t want to send Ron and Hermione into the fray, knowing they’ll likely be hurt—especially given Voldemort’s propensity for taking hostages. Oh yes, Dumbledore planned every detail very carefully indeed.
So, the next question to answer is why Dumbledore had Quirrell provide one of the protections if he so clearly suspected Quirrell by that point? Not only does this make Quirrell’s job that much easier—by allowing him to know what the other protections are—but this could also hinder the trio. Sure, they took out a troll before, but as McGonagall says in the first movie, it was “sheer dumb luck.”
I believe that Dumbledore did this with the intention of protecting Ron and Hermione—he needed Quirrell to get to the Mirror without issue so only Harry would face him. If Quirrell hadn’t been privy to the protections surrounding the Stone, he might have actually been stumped by them—maybe he’s terrible at chess! (Side note: I now have a great mental image of Quirrell playing countless chess matches against Voldemort as practice for this one.)
If Quirrell couldn’t get past the chess board or any other obstacle, he would have run into the entire Trio there. And he likely would not have hesitated to kill them. To reiterate, Ron and Hermione have no protection from him, and Dumbledore would have wanted to prevent them facing off against Quirrell. Hence, Dumbledore includes Quirrell in “protecting” the Stone in order to make Quirrell’s job easier and make sure he’s well ahead of the Trio.
It’s also worth noting that Dumbledore probably supervised these protections extremely closely. He likely did not tell the professors his reasons, but I could believe he suggested the individual protections to each professor and made a sufficiently convincing case that they listened. He probably ensured that Professor Sprout would mention Devil’s Snare in class, since that plant seems to be rather different from the usual curriculum in Herbology (the younger students don’t generally deal with deadly plants).
The exception to this might be Snape’s puzzle—that one seems to fit Dumbledore’s plans so exactly that it’s hard to believe it wasn’t micromanaged. Perhaps Dumbledore trusted Snape enough to reveal the plan. But I think it’s more likely Dumbledore just told Snape exactly what had to be done without explaining himself, and Snape obeyed because he knew to trust Dumbledore despite his secretive ways.
Dumbledore’s Invisible Hand
Now that we know Dumbledore’s end goal—to have Harry face off against Quirrell to gain some valuable experience—let’s examine how he imperceptibly influenced events for an entire year to get there.
Dumbledore has sources that keep him informed of Voldemort’s doings; in Book 2 they let Dumbledore know that Voldemort “is currently in hiding in the forests of Albania.” (CS328) So when these sources inform him that Voldemort is gone from Albania in 1991, Dumbledore knows to fear for the Sorcerer’s Stone.
He also knows that Quirrell was recently there, so Dumbledore probably suspects him to some degree. But Dumbledore is not sure and wants to find out what’s up. He decides he wants the race for the Stone to happen at Hogwarts, where he can keep an eye on things. It’s probably at this time that he concocts his plan to have Harry face off against Voldemort, so he has Hagrid pick up the Stone from Gringotts, in full view of Harry, giving Harry the first clue.
There is really no other reason why Hagrid was picking up the Stone as part of his and Harry’s trip to Diagon Alley, considering wizards can just Apparate to Diagon Alley whenever they need to. Admittedly, the one bit that cannot be easily explained away is Quirrell attempting his Gringotts robbery hours after Hagrid retrieves the Stone. I suppose one could come up with a convoluted explanation of how Dumbledore dictated the timing of this event, but I am comfortable calling this one a coincidence and moving on. I set very little store in coincidences in Rowling’s world, but they do happen, and on those rare occasions I’ll accept them as such.
Then, as soon as the school year starts, Dumbledore proceeds to set Quirrell (if Quirrell is indeed Voldemort’s agent) on the trail of the Stone. At the Start-of-Term Feast, Dumbledore makes a very public announcement that “the third-floor corridor on the right-hand side is out of bounds to everyone who does not wish to die a very painful death.” (SS127)
Honestly, he might as well have whispered in Quirrell’s ear, “Psssst! That’s where I’m hiding the Stone!” Even Percy notes how strange this announcement is, “because he usually gives us a reason why we’re not allowed to go somewhere.” (SS127) But Quirrell takes the bait—hook, line, and sinker. The very next morning, Harry and Ron are rescued on the third-floor corridor “by Professor Quirrell, who was passing.” (SS132)
Dumbledore notices this, and tells Snape, “Keep an eye on Quirrell, won’t you?” (DH679) We don’t know precisely when this “Prince’s Tale” flashback takes place, but since Snape is ranting and raving about Harry, we can assume it was around the second or third week of the term. Dumbledore’s plan is working beautifully, since a week into the school