Music byThe Horrie DargieQuartetArranged byVern Moore

There is no track listing in the film's credits, but Colin Bennett in his review of the film for The Age on 16th December 1966 provided these details:

Horrie Dargie's quintet contributes a jolly version of "Click Go The Shears," Ian Turpie has a romantic ballad and Howard Morrison a Maori number. But it is Vern Moore's catchy "Christmas Time Down Under," sung by Miss Newton-John, that steals the sound track.

Arranger Vern Moore was a member of the Horrie Dargie Quartet/Quintet (see below for photo).

Horrie Dargie was extremely popular in Australia, as a musician and harmonica-player, and as leader of an eponymous Quartet and Quintet and the Dargies. He was the first Australian to achieve gold record status, selling 75,000 copies of a 1952 farewell concert recorded before the band headed off to England. His wiki is here.

It almost goes without saying that Olivia Newton-John turned into an internationally recognised singer, entertainer and actor, and her wiki, one of many reference points for her career, is here. See the galleries for photos of her performing the song.

Maori singer Howard Morrison (later Sir) appeared regularly in Australia in the "Howard Morrison Quartet", and after ten years of concert, TV and nightclub work, struck out on his own as an entertainer in 1965. He was based in Rotorua and he subsequently turned up in a New Zealand film in 1966, Don't Let It Get To You, which reunited him with his Funny Things co-star Tanya Binning (and Australian pop idol Normie Rowe). He enjoyed a long and popular career in New Zealand as a singer and entertainer. His wiki is here.

(Below: Howard Morrison).

Ian "Turps" Turpie was a teen singer and performer who became a familiar entertainer, actor and television personality on the domestic Australian scene. His wiki is here. He died in March 2012 and there were many obituaries published, including this one for Fairfax here.

Here's Turpie relatively early in his career, and in an appearance in 1965 with Olivia Newton-John on Sing, Sing, Sing, a popular national teenage music show.

The National Library of Australia contains no records indicating the song sung by Olivia Newton-John was ever released, even as print music, but an excerpt fromthe film running 2'24" featuring the song can be found on YouTube, at time of writing, here. And here are the lyrics:

(Chorus of several kids:It's Christmas,We're making some Christmas pudding, repeated)

Olivia Newton-John:

See the sun in the skyAlways riding highAt Christmas time down under

It will be no surpriseTemperature will riseAt Christmas time down under

This is a festive timeAnd we have no rainSanta is dressed up fineHere he comes again

At the time and the placeThey come face to faceAt Christmas time down under

Doesn't seem quite the samePlaying winter's game in the sun

The only snow we have is on our Christmas treeThe Southern Cross is not the Northern StarWe like to make believeWe hear those jingle bellsIt doesn't really matter where we are

We can look to the skyAnd see the reason whyIt's Christmas time down under

It's so wide, its so blueYou'd see the reason tooAt Christmas time down under

The world seems the wrong way roundSomeone made it soSomeday we're up side downAsk the man who knows!

It's his birthday todayHe came here to stayAt Christmas time down under

It's up over for meDown under when I seeClear blue sky!

(Below: Horrie Dargie and his band in The Age, 17th September 1965 - arranger for the film Vern Moore is centre - and below that an earlier incarnation of his Quartet c.1960s, and below that an even earlier incarnation of the band at the time the first gold record by an Australian band was released on 10" by Diaphon, including the record cover).