Thanks Kazbah. I googled our registration body (that I am submitting this to) and "style guide" but nothing came up. I did find this though:
(Still don't get how to do the quote thingy)

Capitals are used sparingly. The generic use of a term is not capitalised, but when it forms part of a title it takes a capital letter:

Master of Architecture / a master's degree can be taken
Professor Peter Wright / Peter Wright is a professor of English
Crime Research Centre / the centre opened in 2005

When referring to our own University in short and in full, the word 'University' is capitalised:
The University of Western Australia is considered one of the top universities in Australia. The University continues to rate very highly in the Good Universitites Guide.
When referring to other universities, lower case is used, except as part of its proper title:
The exhibition will take place at this University, Murdoch University and two overseas universities.

When referring to UWA faculties, the word 'faculty' is capitalised in both the full title and subsequent occurrences:
The Faculty of Life and Physical Sciences welcomes new students and encourages them to participate fully in the activities of the Faculty.
However, the word 'faculty' is not capitalised when referring to the term in general:
A faculty can choose to expel a student who has cheated.

For headings within a document, sentence case (with the first word only capitalised) is used except where the name of an entity forms part of the heading:
Media and advertising expenditure
Statement of compliance with the Record Keeping Plan

The subject areas of specific majors and honours degrees are capitalised, as are WA Certificate of Education courses:
a major in Botany
honours degree in Molecular Biology
WACE English

Schools and discipline groups are always capitalised but not the words 'school' or 'discipline' when used generically:
the School of Psychology / students should contact their school office
the discipline of History / staff of the History discipline
lectures may be given by staff in other disciplines

I think I get it, but am still a bit unsure about the titles of the professionals in the context of "The diagnosis was given by a paediatrician....". I'm talking about a specific paediatrician but not including his name, and I guess therefore sort of referring to the profession title in general. This is so tricky and my brain is sooooo tired!