Thanks for that. Nice to see some Kirker's finally showing up on the Vic BDM, last time I looked there were none (though that was awhile ago).
There are some Rea's Kirkers in the NZ BDM but as far as I know they are not related to my William Kirker.
When I first started trying to trace this family I wrote to every single Kirker in New Zealand. Quite a few replied back and it seems there are 2 separate Kirker families in NZ. One is quite well to do and many of them are Doctors,Lawyers, Artists. The other Kirker family (mine) is the other branch. We did discuss a possible connection but if there is one it goes back to before NZ and this family's NZ ancestor was definitely not a brother or a cousin of William. (pity).
I will keep searching both through the NZ and Australian ends to see if anything turns up and maybe even go back to all the places I contacted before to see if there is any new information. Looks like I'll be sending lots of emails to all the Australian records offices and historical societies again
I have also been thinking about writing to every Kirker in Australia - maybe one of them will know something.
Looks like the Ireland thing is probably a dead end then at the moment. Would have been nice to have traced William Kirker (senior) and Mary Brown to see where they ended up and if they really were his parents.
Thanks everyone for all your help.
Looks like I am for now back to square one and starting all over again.