"We're goin' ter Diagon Alley, where yeh'll buy yer things."

"Ooh."

"But now we'll sleep, it's late an' I'm tired."

"Yeah."

"So—g'night!"

"Goodnight."

"—oh, I almost forgot—" From a pocket inside his overcoat he pulls an owl—a real, live, rather ruffled-looking owl—a long quill, and a roll of parchment. He sits back down from a moment and, with his tongue between his teeth, scribbles a note that Dorea can read upside down:

Dear Professor Dumbledore,

Given Dorea her letter.
Taking her to buy his things tomorrow. Weather's horrible.
Hope you're Well.

Hagrid

He rolls up the note, gives it to the owl, which clamps it in its beak, goes to the door, and throws the owl out into the storm.

"...Were they okay in there?"

"The owl? Aye, it's warm an' snuggly, he's prob'ly upset that I made 'im go out in this storm."

"...Fair."

Hagrid does not take long to fall asleep after that. The shack is much warmer with the magic fire over there.

Yeah. Zzzzzzzz...

She will wake up to the sounds of an owl rapping on the window.

...She muzzily blinks sleep out of her eyes and goes to open the window.

It's a bright and clear day out, the storm having abated completely. The giant is still asleep on a collapsed sofa, snoring.

The owl swoops in and drops a newspaper it had been holding in its beak on top of Hagrid, who doesn't wake up. It then flutters onto the floor and begins to attack Hagrid's coat.

"...Hagrid?"

"Pay him," Hagrid grunts into the sofa.

"How?"

"He wants payin' fer deliverin' the paper. Look in the pockets."

...She rummages in the coat pockets.

Hagrid's coat seems to be made of nothing but pockets—bunches of keys, slug pellets, balls of string, peppermint humbugs, teabags... there, a handful of strange-looking coins.

"Give him five Knuts," says Hagrid sleepily. 

"Which ones are those?"

"The little bronze ones."

She extracts five bronze coins and gives them to the owl.

It bows its little owl head and takes off. Hagrid yawns loudly, sits up, and stretches. "Best be off, Dorea, lots ter do today, gotta get up ter London an' buy all yer stuff fer school."