William Hayden Daniel birth registered Axminster, Devon, 1841 Q3 10 8
Mary Elizabeth Daniel birth registered Islington, London, 1846 Q1 3 262
Maria Jane birth registered Shoreditch, 1853, Q4 1C 160
Rosa birth registered Shoreditch, 1856, Q4 1C 144

In the UK 1851 census they are living at 55 Herbert Street, Shoreditch, Tower Hamlets, London
John; Head, 38 (1813) a Customs Officer, born Axminster, Devon
Marie, Wife, 35 (1816), Embroidress, born Tiverton, Devon
John Isaac Pryer, son, 11 (1840), Scholar, Axminster, Devon
William Hayden, son, 9 (1842), Scholar, Chardstock, Devon
Mary Elizabeth, daughter, 5 (1846) Scholar, Islington, Middlesex

There is the death of a Maria Daniel in Shoreditch, 1857, Q3 1C 116, this could be either the mother or Maria the child : also a John Edward Daniel also in Shoreditch 1854, Q2 1C 110. It could be that these deaths are not your John & Maria but it could explain why the children emigrated

John Isaac Pryer married in 1865 in Shoreditch Q1 1C 298 to Phillis Mary Alison. They are in the 1871 census living at Mildmay Road, Islington
John I P, Head, 30 (1841) a Clerk, born Devon
Phillis M, wife, 26 (1845) born Middlesex
Henry Daniels, Uncle, 53 (1818), Axminster, Devon

After Maria died, John Daniel remarried Anne Branka, doughter of Mary A Branka a widow but then both Anne & John Daniel died.
The 1861 census shows Isaac Daniel (John Isaac Pryer?)and Rosa Daniel (Baptised 18 June 1857 City Road Congregational Chapel, Parents John and Maria Daniel - Customs clerks) and says that she (Mary A Branka) is the Executrix of John Daniel who died 11 March 1861. Natiuonal Probate Caendar for 12 April 1861 shows Mary A Branka being granted probate for John and Anne Daniel who died 13 March 1861.
Thus John Isaac Pryer and Rosa were together in 1861 but where were William Hayden and Mary Elizabeth.

I found a request for information about them on an Australian site that said they had imigrated as unaccompanied minors in c1856. A William Hayden Daniel was declared bankrupt in Dundee NSW in 1867 (see Sydney Morning Herald Sun 23 March 1867). I'd like some proof that William Hayden and Mary Elizabeth did go to Australia so I can close that part of my tree.

John Daniel (b1813) parents were John Daniel (b Beaminster, Dorset 1761) and Mary Elizabeth Hill who were married at St Sidwells, Exeter on 4 October 1810. John was a currier in Axminster.
If you are tracing this family you can find more information at http://www.rupertwilloughby.co.uk/dorset-families

KGS: I have found your post 10 years later! It is very helpful. Thank you. Are you still researching siblings William and Mary Elizabeth Daniel? I have started. Mary was my 2x great-grandmother. Mary and William did come to Australia, probably with their uncle and aunt, who had no children. Uncle James Hill Daniel (1817-1861) was a Master Mariner on the London to Melbourne-Sydney run in 1852. He married in 1848 at St George-in-the-East, Tower Hamlets, where his brother John (1813-1854) and family lived. James lived at 10 Cannon Street Road in 1848. From c.1854-1856 James sailed on NSW coastal ships. In 1856 he left the sea, settled in Walcha NSW with his wife Jane (1811-1894). I suspect that William and Mary arrived then. According to family stories, Mary was 16yo when she came to Walcha, but that does not fit with other events. I am happy to share more, if you have not already found this information.