The Australian-English noun stickybeak denotes an overly inquisitive person, who pries into the affairs of others.
—Synonyms: nosey parker and Paul Pry.

The primary meaning of the noun stickybeak is: the nose of an overly inquisitive person—cf. in particular quotations 1 and 2 below.

The earliest occurrences of the noun stickybeak that I have found are as follows, in chronological order:

1-: From the following poem, published in the Evening News (Sydney, New South Wales) of Saturday 17^th October 1914:

THE LUST OF BLOOD.
TRANSFORMATION OF MR. LATH.

A man of piety was Lath—
A timid, gentle soul;
He walked the straight and narrow path
To a celestial goal.

His garb was sober, even sad,
In keeping with his face,
For from the time he was a lad
He’d never “gone the pace.”

A quiet suburb held the nest
Of Lath and wife and child.
The three were called the very best
Within that district mild.

To church on Sundays would they go,
And join in prayer and praise.
They deemed all dancing very low,
And shunned the ragtime craze.

Alack the day the war broke out,
The loud alarums rang;
“Arm! arm!” uprose the loyal shout;
Lath heard it with a pang.

“Oh! why should men,” he asked in grief,
“Their brothers seek to slay?
I hope it will be very brief—
The Lord their hands will stay.”

With pain, the truth must now be told,
A sticky-beak he grew,
Wherever war editions sold,
There Lath would coppers strew.

The cables from the front he’d scan
In feverish, guilty haste;
And gloat, poor wicked, sinful man,
On tales of towns laid waste.

Atrocities of hideous kind—
On woman, girl, or boy
Were balm to his ensanguined mind,
And brought him fearful joy.

Of blood he talked, of blood he dreamed—
Of thousands done to death;
And waking, oft for blood he screamed
With all his power of breath.

For weeks, he revelled in this bath
Of mind-enveloped gore;
The neighbors said, “Poor Mister Lath,
How he does feel the war.”

By what it feeds upon, ’tis said,
The appetite will grow,
And, presently, when news he read,
He voted it dashed slow.

“There’s nothing in the beastly rags,”
He scorned, in bitter flood;
“The battle much too slowly drags,
Why isn’t there more blood?

I want Germania’s pride laid low,
And carnage on her coasts.
I want to see the rivers flow
With blood of Touton hosts.

I want”—but ere his tale was told,
There came two policemen stark,
And in a taxi he was bowled
Right out to Callan Park. *

And there he sits, from morn till eve,
And soldiers makes, of mud;
His fall from grace we deeply grieve,
Peace to the man of blood.

—J. N.

* This refers to Callan Park Hospital for the Insane, in Lilyfield, a suburb of Sydney.

2-: From a letter to the Editor, by ‘a commercial man’, published in The Bendigo Advertiser (Bendigo, Victoria) of Thursday 11^th January 1917:

I too like children singing, because they sing from their hearts, and no spirit of “I can sing” in it. Thus we get it pure and wholesome. Certainly, let us have more children’s choirs, or any other items to uplift our city in this department. It is dead enough, heaven knows, and I too get tired of pictures and long for something else with “soul” in it. I said go on Mr. Bindley with your good work. I say it now, and if you got up a choir for Easter Day evening in the Lyric on behalf of the fair, I am sure a good sum will be realised, but for heaven’s sake keep the management from putting in its sticky beak and interfering with the conductor. I say give Mr. Bindley that free hand and I know the result.

3-: From one of the unconnected paragraphs making up the column They Say, published in the Portland Observer and Normanby Advertiser (Portland, Victoria) of Monday 10^th September 1917:

That the role of mediator is always an unenviable one. Someone is bound to call him “sticky beak” and accuse him of bias.

4-: From The Independent (Benalla, Victoria) of Friday 28^th September 1917:

Our Troubles
The Independent has been struck with amazement at the alacrity displayed in a certain quarter to make us famous. We have always endeavored to maintain the kindliest of relations with the “birds of our own feather” particularly, to avoid as a deadly sin any spirit of hate, which properly belongs to Sheol. That little esprit de corps is evidently not reciprocated in every case. How nice, for instance, to extend the hand of brotherhood to another when the wheels of his whapperchoke refuse to revolve; how like music soothing the savage breast the voice of a rival over the phone, “You’re welcome as the flowers in May to all I’ve got, from the smallest heap of ‘pi’ to the big inker.” Sad to discover in an hour of trouble that old pals to whom you look to act the gentlemen suddenly develop into hangmen, who do not mind fixing the noose for the shuffle. It is good business on the part of “sticky beaks” to be careful where they put those beaks. All men have their troubles. We have ours just now. A temporary friction between friends will quickly disappear if wise counsels prevail. We have neither the desire nor the intention to aggravate an unfortunate position that has arisen during the past day or two. The parties concerned may easily adjust matters if only meddlesome microbes keep their machinations to the sewer, their natural abode of hate and malice. We deeply appreciate the many kind expressions tendered by friends, among whom we cite Mr John G. O’Shea, who throughout our nine years’ sojourn here has acted the part of a true brother pressman.

The word stickybeak soon came to be also used as a verb meaning to pry, to snoop. For instance, the verbal noun stickybeaking occurs in the following from Smith’s Weekly (Sydney, New South Wales) of Saturday 20^th November 1920:

THE FORUM — AND AGIN-UM
Devoted to the Terse Discussion of Claims, Grudges, Grievances and Complaints

[…]
Curiosity Rebuked
Some people are not satisfied with reading a book; they have the impudence to try to discover how much they were overcharged for it. A book bought recently was labelled 10/6. Under label was a wafer marked 7/6; under that again one marked 6/-. The bedrock price, 5/-, was printed on its wrapper. One Sydney bookseller now marks his disapproval of sticky-beaking by cutting the price off the wrapper. It saves argument, he says.—M.