What a can of worms! ...... . It would not surprise me if he emigrated as Heinrich rather than Jurgen. He called himself Henry and Harry in Australia.
Yes, Neale's summary is spot on.
May I mention that just a quick look at births as INDEXED at NSW BDM online, for your couple, I can clearly see that he was not just Henry and Harry but he did use his full name.
Here's seven N.S. Wales births
, remembering that NSW BDM online index originates from a volunteer project in the 1930s… Volunteers reading well worn pages, longhand scribble, ink bleeds, torn corners etc and doing so under natural light only to provide NSW BDM with an INDEX for the first time...
So for BIRTHS for this family, the online index gives Agnes and/or Agnes A as mum’s name, and variations on Harry’s given names.
1878, reg’d Albury, #7623, Caroline, Dad as Turgen H BURMEISTER, Mum as Agnes A
1880, reg’d Albury, #8399, Frederick W, Dad as Henry BURMEISTER, Mum as Agnes A
1881, reg’d Albury #9265, Alice, Dad as Henry BURMEISTER, Mum as Agnes
1884, reg’d Albury, #12197, Ernest N, Dad as Turgen H BURMEISTER, Mum as Agnes A
1885, reg’d Albury, #12649, Samuel A, Dad as Henry BURMIESTER, Mum as Agnes A
1887, reg’d Corowa, #13940, William J, Dad as Jargan H BURMIESTER, Mum as Agnes A
1889, reg’d Corowa #13802, Agnes A, Dad as Jurgen H BURMEISTER, Mum as Agnes A
1892, reg’d Corowa, #11707, Emily B, Dad as Jurgen H BURMEISTER, Mum as Agnes A
So Emily's b.c. should list her details, her parents details and details too for her older siblings.
JM