Harry’s recollection of the dream is extremely fuzzy. The full quote is rather long, so here’s a brief summary of what he remembers:
Three people were present – Voldemort, Wormtail and somebody he doesn’t recognise (the Muggle, Frank Bryce) – as well as Nagini.
[In the movie adaptation, Barty Crouch Jr. is also present at this meeting. We know he’s not in the book, because Voldemort says “By that time, my faithful servant will have rejoined us—”, clearly referring to Crouch. It would be strange to say this if Crouch was in the room with them.]
Voldemort and Wormtail had been talking about somebody’s murder (Bertha Jorkins, although Harry doesn’t remember the name) and plotting to kill someone (him).
This took place in a darkened room, and Voldemort was sitting in a chair.
Alone, these probably wouldn’t have been a huge amount of use to Dumbledore, but they would have backed up his existing theories. We later learn that Dumbledore has been carefully monitoring disappearances potentially connected to Voldemort:
“The years of Voldemort’s ascent to power,” he said, “were marked with disappearances. Bertha Jorkins has vanished without a trace in the place where Voldemort was certainly known to be last. Mr. Crouch too has disappeared... within these very grounds. And there was a third disappearance, one which the Ministry, I regret to say, do not consider of any importance, for it concerns a Muggle. His name was Frank Bryce, he lived in the village where Voldemort’s father grew up, and he has not been seen since last August. You see, I read the Muggle newspapers, unlike most of my Ministry friends.”
— Chapter 30 (The Pensieve)
So he already knows about the deaths of Bertha Jorkins and Frank Bryce; Harry’s dream wouldn’t tell him that. (Although when presented with her name, Harry might have confirmed his memory.)
The other details are unlikely to be of significant use to Dumbledore, as the rest of them are either unimportant (darkened room) or can be easily guessed (Voldemort wants to murder Harry).
But if Dumbledore had an accurate recollection of Harry’s dream, then things might have been very different.1 There are several key lines that hint at Voldemort’s plan:
Voldemort is still dependent on Wormtail.
“Your devotion is nothing more than cowardice. You would not be here if you had anywhere else to go. How am I to survive without you, when I need feeding every few hours? Who is to milk Nagini?”
This means that if Wormtail can be captured or injured, Voldemort would be extremely vulnerable. Still formidable, but not at full strength.
Voldemort and Wormtail expect to stay at their current location for at least a week.
“My Lord, may I ask how long we are going to stay here?”
“A week,” said the cold voice. “Perhaps longer. The place is moderately comfortable, and the plan cannot proceed yet. It would be foolish to act before the Quidditch World Cup is over.”
Combined with the knowledge that Frank Bryce has been killed, Dumbledore may have been able to travel to Voldemort’s location and capture him before his resurrection.
There would be a Death Eater at Hogwarts.
“One more murder… my faithful servant at Hogwarts…”
This tells Dumbledore that Voldemort is already in contact with at least one other Death Eater, and plans to have a spy at Hogwarts this year.
Plenty of candidates – if not Snape, then Karkaroff via the Triwizard Tournament (although both seem unlikely). But Moody, and the fact that he was attacked before he arrived, might have drawn extra scrutiny. Et cetera.
Dumbledore works this out later, when Harry’s name comes out of the goblet, but he would have known a lot sooner and potentially guarded the goblet more carefully.
So perhaps an accurate copy of the dream wouldn’t have stopped Voldemort completely, but it probably would have slowed him down considerably.
1 If Harry had told Dumbledore, then perhaps Dumbledore could have taught Harry how to use the Pensieve, and extracted the information that way. The Pensieve records reality, not your viewpoint or memory of it. (from the first question in this J.K. Rowling interview.) Alternatively, some of the dream-reading equipment he uses in Order of the Phoenix.