This is the Victoria, Australia, BMD Index for searching.
http://www.bdm.vic.gov.au/home/family+history/search+your+family+history/I just typed all this up so will post - a couple more children, I think. And knowing the year of registration also helps. If they were in essence a Scottish family, the names of the children could well be largely keeping to the tradional Scottish naming pattern:
BIRTHS: DICKSON (Reg Year / name/ reg Nr/ mother (and her ms)
1862: Robert Patrick, 5542 - Charl (Stephenson)
1863: Alexander Campbell 16684 - Charlotte (Stevenson)
1864: William Muirhead 21771, - Charlotte (Campbell)
1866: Charlotte Mary Ann J , 21311 - Charlotte Cather (Campbell)
1868: Mary Ann Stewart 2619 - Charl Cath Cam (Stevenson) **
(twin?)1868: Charlotte Anna Campbell 2620 - Charl Cath Cam (Stevenson)
(twin?)1871: Lilias Winefred, 9024 - Charlotte (Stevenson)
1872: Un-named Male, 23238 - Charlotte (Stevenson)
1875: Un-named male 2313, - Charlotte (Stevenson)
1877: Un-named male 2535, - Charlotte (Stevenson)
DEATHS: DICKSON 1865: William Muirhead 1067 - Charlotte Catherine (Unknown)
1868: Alexander Campbell 1108 - Charlotte Catherine Campbell (Stevenson)
1873: Charles Airlie, 1081 - Charlotte (Stevenson)
1867: Charlotte Mary Ann, 1472- Charlotte Catherine (U)
1869: Mary Ann Stewart 4098 - Charlotte (Stevenson)
The 3 unnamed male BIRTHS all register the VIC place of birth as : ESSENDON - not a million miles away from Newport VIC.
Based on the names of the children, I'd suggest Robert's own parents could be Robert DICKSON & Mary Ann STEWART.
The names of Charlotte's parents if in pattern, would be 1st daughter and 2nd Son; daughter's position is bang on, but it looks like they deviated a bit and put the 1st and 2nd son pattern name into the one name for first born son. 'Alexander Campbell' could be the name of a grandparent or brother of Charlotte.
Cheers
AMBLY