The jocular Australian-English expression the ant’s pants denotes an outstandingly good person or thing [cf. footnote].

Resting on nonsense and on alliteration and assonance, it is a variant of the synonymous jocular expressions, of American-English origin, based on various parts of animals’ real or fanciful anatomy and other attributes, such as the bee’s knees and the cat’s whiskers.

In fact, the text containing the earliest occurrence of the ant’s pants that I have found associates it with the American-English expressions the bee’s knees and the cat’s whiskers—this text is the column The Moving Picture Show, published in The Sun (Sydney, New South Wales) of Tuesday 22^nd May 1928:

Hands Off China
Noticing that “official circles in Washington are very uneasy” lest the Japanese should act in Manchuria in a way detrimental to the “rights of China,” Peter sought an explanation.
“Say, bo,” said the Secretary of State, “ain’t it just turrible to think that a lotta pore guys like them Chinks kaint run their country how they darn well please without them other fellers interferin’! I’ll tell the world!”
“It’s the bee’s knees!” said Peter’s representative.
“Notatall!” said the Secretary of State frowning. “Sa-a-ay! How’d you like it in Australia if a Victorian army, under that guy Bavin, was marchin’ on Sydney, the capital of Melbourne, an’ another army uv Brisbanians under McCormack, was marchin’ on Noo South Wales, the capital of the Northern Territory, an’ O’Grady, with his Tasmanians, was hoverin’ on the flanks of both of ’em near Fremantle, the capital of Hobart, an’ Sir Joe Cook was sendin’ out manifestoes of defiance to the lot of ’em, from Bruce, the capital of Page—”
“It would be the cat’s whiskers!” exclaimed Peter’s representative.
“If all that fun was goin’ on,” went on the Secretary of State, “an’ them Noo Zealanders was to get sick of it, and you killin’ their relatives every now an’ then, an’ come an’ try to stop you—”
“It would be—” began Peter’s representative.
“Say, bo!” snarled the Statesman, “You think you’re the ant’s pants, don’t you?”
“Sure!” said Peter’s representative. “But don’t you heave that ink-pot, sir! You ain’t in Nicaragua naow.”

The meaning of ants-pants is obscure in the sports column Prickly Pellets, published in The St. George Call (Kogarah, New South Wales) of Friday 1^st June 1928:

Saints great day at Earl Park. Did the hat-trick. Line not crossed in either grade. Wonderful defence!
Owing to there still being a doubt as to the color of Bosso’s socks, it has been decided to have them exhumed for further inquiry, to take place in Boorowa. When will it end?
Look out for Jack Yule’s ants-pants, he has hired a special pair from a Chinese cook-house for the occasion during travelling!

The expression the ant’s pants then occurs in the following from The Forbes Advocate (Forbes, New South Wales) of Monday 9^th July 1928:

THE GOLF CLUB BALL.

The watchword to-day in Forbes is, “See You on Thursday Night.” This means seemingly that most of the local dancing population is going to the Golf Club annual ball on the night mentioned. Folk remember how successful these events have invariably been, and the next club function is looked forward to with keenness and pleasurable anticipation. According to the club committee this year’s event is going to beat bogey by a street. “It’s going to be the ant’s pants,” we are assured by several who should be in a position to know. Owen’s orchestra is being brought from Orange to supply the music, and no stone is being left unturned which will help toward success.

The expression occurs as the ants’ pants, together with the cat’s whisker and the fly’s eye, in the column The Moving Picture Show, published in The Sun (Sydney, New South Wales) of Tuesday 16^th October 1928—the Italian Fascist politician Benito Mussolini (1883-1945) was Prime Minister of Italy from 1922 to 1943:

The Presentation
Signor Mussolini’s own name was on the list for a £20 prize, when he gave out the prizes to farmers for increasing the average of their grain output. Mussolini trebled his own wheat output.
“I have now come,” said il Duce, “to the last on the list—step forward Coltivatore Benito Mussolini and receive the reward of industry!”
The Coltivatore then stepped forward, turned, bowed, blushed, and kneeling upon one knee, kissed the boots of Il Duce, who patted him on the head and then with his left hand, placed the £20 in the right hand of the Coltivatore.
“Benito,” he said, “you have been the good boy—stick to the plough and never go to sea, and you may remain the ruler of the King’s navee. I am proud of you, Benito. I get prouder and prouder of you every day. I am, indeed, so infernally dashed charmed by you—” here Il Duce broke down with emotion, and the Coltivatore then stood on his head with glee and replied:—
“Oh, mio carissimo! For this praise I shall serve you till I die! You are the ants’ pants, the cat’s whisker, the fly’s eye, and the bally limit. Hooray for me—I mean you!”
“You are dismissed,” said Il Duce. “Take care of the £20, and don’t spend it all on chianti.”
The Coltivatore then got up, brushed the dust off himself, turned again to the audience and Il Duce resumed his speech:—
“Now that that is over, my young lions, bring in all those Cattivi blokes that didn’t work hard enough to win a prize—and tell Giuseppe Jackogorilla, the captain of the guard, to bring in the castor oil!”

Note: There is no relation between the Australian-English expression the ant’s pants and the American-English phrase to have ants in one’s pants, meaning to be fidgety or restless.