Just a note that the GRO index per FreeBMD shows the Julian Carne Tabb baptism I referred to as Juliana Carne Tabb (after some dithering with name corrections), 1842 Truro, but still no later reference to be found.
Oh, no, interesting: in 1851, Anc'y shows Julianna no surname (I searched just for jul* in Cornwall born 1841-43), born c1842 Kenwyn, living with Richard and Sarah Carne (mistranscribed Corne), obviously Juliana's grandparents, in Kenwyn. No surname is shown on the original census image. There is also a Robert Carne next door, who would be a son of that couple.
This would be consistent with her mother being deceased, so I think the William Tabb + Elizabeth Carne marriage is very likely correct and Julianna is a sister of your William. So if William Jr's birth cert confirms that mother, this info should help.
And in 1861 she is transcribed as Julian Tabb, born c1842 Kenwyn Cornwall, in East Stonehouse, Devon. (Moving over to the Plymouth side was very common in that era.)
(Just for ruling out: in 1871 she is not, as I was first going to say she might be, Julianna Woodley, married to Thomas with two children, born c1844 Kenwyn, in Kenwyn in 1871. That marriage was Thomas Woodley + Julia A Oates 1866 Truro, Juliana Oates being in the 1861 census.)
There is also a Jane Tabb with Juliana in East Stonehouse in 1861, aged 24, born Kenwyn Cornwall.
Richard Carne married Sarah Dinnis in Kea 1803.
Richard and Sally Carne had a daughter Juliana Carne in Kea 1807. That is the only baptism to Richard and Sarah/Sally Carne showing in the database. She would be the recent source of the name of Julianna Tabb.
Also note that the Catherine Tabb I referred to died at age 4 months in St Clement in 1844:
http://www.cornwall-opc-database.org/search-database/more-info/?t=baptisms&id=977842http://www.cornwall-opc-database.org/search-database/more-info/?t=burials&id=1739920