Not unusual not finding people on the 1901 electoral roll. Compulsory voting in Australia was adopted in Queensland in 1915 and subsequently adopted nationwide in 1924.
I note that Charlotte's parents' names are on the death index and someone had to give Charlotte's their names etc to the undertaker - perhaps taken from previous certs.
Have you seen the ALEXANDER /POTTER marriage cert in 1930? Surely if Charles was Charlotte's natural child, he would be listed, not by name, but as living issue.Have you the above cert?
I note that on Charles' burial record Beames is again part of his name
POTTER, Charles Beames
Cemetery Woden Date of death unknown
Date of burial Tuesday, 7 June 1955
Headstone Anglican AN/H/B/001A
Certainly frustrating for you not finding Charles Beames' birth details
Cando