Can't help with the actual marriage and you may already have these snippets.
Robert is listed in New South Wales, Australia, Government Gazettes, published 1882. p20 (I think this is the page number for a list of registrations and certificates of doctors)
Registered Jul 1, 1872, cert #713
Peed, Robert Jephson
Lic R. Coll. Sur. Irel. 1867
(I'm assuming this means he was gained a Licence of the Irish College of surgeons in 1867 and was granted a certificate to practise in NSW in 1872)
Trove:
https://trove.nla.gov.au/newspaper/article/13264339The Sydney Morning Herald, Mon 7 Oct 1872
DEPARTURE FOR ENGLAND.
October 2 Nineveh, ship, 1174, Barnett, for London
Passengers Miss Barnett, Mrs Harrison and 4 children, Dr. Peed, Mrs Peed Mr. Harrison, Mr. CurrBaptism and civil registration of son:
https://www.familysearch.org/en/search/all-collections/results?q.surname=peed&q.givenName=henry&q.birthLikePlace=IrelandHenry Joseph Peed
Father's Name Robert I. Peed
Mother's Name Julia Sophia Nicand
Birth 10 Feb 1877
Event Place Wexford, County Wexford, Ireland
Event Place (Original) Wexford, Ireland
https://www.census.nationalarchives.ie/reels/nai003705490/Census of Ireland, 1901
Living at: Cullenswood, Elmgrove and Elmpark, Rathmines & Rathgar East, Dublin, Ireland
Sophie Peed, head of household, widow, 60, born Switzerland
Henry Peed, son, single, clerk, 24, born Wexford
Judith