The colloquial Australian and New-Zealand phrase not to be able to head a duck is used, in sports, of slowness—in particular as a disparaging comment on a racehorse.

This phrase occurred, for example, in the following from the Daily News (Perth, Western Australia, Australia) of Thursday 2^nd June 1955 [page 23, columns 1 & 2]:

PUNTERS GET WARNING

MELBOURNE, Thurs: Trainer George McCormick last night sounded a warning to punters “specking” * Grand National Steeplechase favourite The Drum in early doubles.
“If it’s wet on Grand National day, The Drum will not start,” McCormick said.
“He could not head a duck on a heavy track.”
Yesterday, however, The Drum was coupled for £5000 each in doubles with Grand National Hurdle fancies Proere, Kadana and Better Law.

[* This is a figurative use of the Australian verb speck, meaning: to search (the surface of the ground) for traces of gold or opal; to discover (particles of gold or opal) in this manner.]

The earliest occurrences that I have found of the Australian and New-Zealand phrase not to be able to head a duck are as follows, in chronological order:

1-: From Sydney Jottings, published in The Richmond River Herald and Northern Districts Advertiser (Coraki, New South Wales, Australia) of Friday 10^th October 1890 [page 4, column 3]—the following is about “the increasing number of the dusky sons of the soil joining the ranks of the professional sprinters”:

A couple of years ago I got hold of one of these dusky gentry, and, from his own account, made sure that I had a real good thing, nothing less than a second Samuels. I built sundry lofty castles in the air, and counted my prospective winnings by nothing short of thousands. I kept this good thing all to myself for some time in as crafty and cunning a manner as possible, all the while fairly gloating over my good luck. At last, feeling that I required some little assistance to mature my carefully laid plans, I rather reluctantly let a sporting boniface into the secret, swearing him to solemn secrecy. He very soon was equally sanguine with me, and together we laid out our programme; but just imagine our disgust, when on giving our “dark horse” a trial, we found he was unable to head a sick duck against whom we matched him. All our castles tumbled down, and we resolved from that day forth to put not our trust in blackfellows.

2-: From Notes by Phaeton, published in The New Zealand Herald (Auckland, Auckland Region, New Zealand) of Saturday 13^th June 1891 [page 6, column 6]:

Of course, Zalinski may be very green; but experience has shown us that the Australians flounder terribly when discussing the Musket family. I remember very well one of the best critics, in the August of 1885, voting Nordenfeldt as fat as a seal, would never be ready in time, and adding that “he couldn’t head a duck.” The son of Musket got there all the same in both Derbies, and ought by all accounts to have also won the Melbourne Cup. Zalinski may bring off a like performance.

3-: From Sporting Notes from Queensland, a correspondence dated Brisbane, Sunday 15^th November 1891, published in The Referee (Sydney, New South Wales, Australia) of Wednesday 18^th November 1891 [page 2, column 7]:

It seems simply wonderful how Coronella has come on since she returned from your colony, where she could not head a duck. On the first day she ran the City Handicap mile in 1min 44sec, and here again she covered the 10 furlongs in 2min 11½sec; so that she must be a much better mare than her southern form would make her out.

4-: From Points, published in The Telegraph (Brisbane, Queensland, Australia) of Monday 23^rd May 1892 [page 4, column 7]:

The Toowong Rowing Club held their regatta on Saturday under very adverse circumstances.
The day was dismal, and the umpire’s boat was about fast enough to head a duck.
It is doubtful whether those on board the Sir Charles Cowper, those on shore, or those at the winning post saw the race to the best advantage.

5-: From Sporting Notes from Queensland, a correspondence dated Brisbane, Sunday 13^th August 1893, published in The Referee (Sydney, New South Wales, Australia) of Wednesday 16^th August 1893 [page 7, column 8]:

Young Buckthorpe […] opened everybody’s eyes by making a determined dash at the leader in the straight. In the Sapling Stakes he could not raise enough pace to head a duck, but he must be a lazy rascal, for when the whip was laid on him yesterday he answered it like a perfect Trojan, and but for being blocked on the rails might have won.