As an infant in World War 2 living in New Zealand, I heard this song
"out of the blue gums, I hear you calling me" It is almost certainly
Australian. Where can I find details: who sang it? composed it? the
words?

"Out of the Blue Gums", as performed by Slim Dusty, is available on a
CD called "Another Aussie Sing Song."

Telstra Country Wide
http://www.telstra.com/countrywide/countrymusic/bio_slim_disc.html?SMSESSION=NO

You can purchase a 2-CD set that contains "Out of the Blue Gums" here:

Country Music Shack
http://www.countrymusicshack.com.au/common/info.asp?cdBarCode=724381418826

An LP record that contains "Out of the Blue Gums" is offered for
auction here:

eBay Australia
http://cgi.ebay.com.au/ws/eBayISAPI.dll?ViewItem&item=2552632278&category=1074

An earlier version of "Out of the Blue Gums" was recorded by Johnny
Wade. This is probably the version that you heard during WWII:

"CD71   Johnny Wade 'Out Of The Blue Gums' (1943-1958)
Featuring His Hawaiians, George Trevare And His Orchestra, and Reg
Lewis and His Prince Edward Orchestra.

Track Listing
1. When I Come Home To You 2. Raimbow Of Dreams 3. It Won't Seem So
Long After All 4. Red Cross Nurse 5. Cherry Lips 6. Out Of The Blue
Gums 7. Sweet Hawaiian Sands 8. The Land Of Sundown 9. Kookaburra
Samba 10. Isa Lei (Fijian Farewell) 11. It Was Written In The Stars
12. No, No. 13. I'm Looking Over A Four Leaf Clover 14. Don't Sing
Ahola When I Go 15. To You Sweetheart 16. Goodbye Hawaii 17. Beg Your
Pardon 18. Sweet Hawaiian Isle 19. The Duke Of Pernambuco 20. Hawaiian
Wedding Song 21. Haere Ra (Maori Farewell) 22. Hello Spring 23. A
Little Ounce Of Sunshine 24. Guilty 25. Its A Long Time Waiting 26.
Meant For Me"

Lyric CDs
http://www.lyriccds.com.au/aussie.htm

If you would like to purchase a CD of the Johnny Wade version (CD71 in
the Lyric catalog, as listed above), you'll find ordering information
here:

Lyric CDs
http://www.lyriccds.com.au/contact.htm

The music and lyrics of "Out of the Blue Gums" were written by George
Trevare, who performed on the Johnny Wade album:

"sheet music - out of the blue gums
 words and music by george trevare"

TradeMe
http://www.trademe.co.nz/Hobbies-Collectables/Music-Memorabilia/auction-3954859.htm

(Note that the TradeMe auction item is no longer available; I have
linked to it because it provided information regarding George Trevare
as the composer and lyricist of the song.)

A rock-and-roll version of "Out of the Blue Gums" was recorded by Owen
Griffiths & Clive Weir & The Rockettes:

Artist:   Collector 7756 A/B 
Title:   Early Rock & Roll From New Zealand Vol 7 & 8 
Media:   2-CD 
Category:   CD - Collector Records 
Other info:   Collector Records Clcd 7756 A/B 
Price:   150.00 SEK...

19  -  Owen Griffiths & Clive Weir & The Rockettes - Out of the blue
gums"

Old Rock
http://www.old-rock.com/album/albuminfo.asp?albumID=2061

(The price on the CD set above is listed in Swedish krona.)

Search terms used:

"out of the blue gums"
"slim dusty"
"johnny wade"
"george trevare"

I hope this information will enable you to listen to the song again.
If anything is unclear, if a link does not function, or if you have a
question about my research, please request clarification; I'll be glad
to offer further assistance before you rate my answer.

Best wishes,
pinkfreud

brilliant,  thanx pinkfreud