Is it appropriate for a PhD candidate to publish a book?
I think it's a very good idea to develop files/manuscript collecting important standard results in one place. To go to the additional trouble (which is much more than one might imagine) of publishing a book with that content, apart from vanity presses, would not be worthwhile for a young academic. Indeed, unless you can do a for-some-reason amazing job of organizing things, since you're not an established expert, have (presumably) no name-recognition, etc., good publishers would not see much reason to publish your book.

But you can assemble a PDF document and put it on-line. And you can revise it as you mature into your subject. Revision is much harder with physical books, or even official "e-books", because many publishers (especially better ones with an established base and style) re-typeset everything into their house style... so correcting typos is not a matter of correcting them in the TeX source, re-typesetting, and re-posting online. :)

EDIT: to clarify the last sentence: Yes, TeX is the current professional standard for mathematicians composing technical documents. It's a mark-up language created by Don Knuth, and donated to the community, in the late 1980s. (There are also WYSISWYG editors.) The older process of typesetting from TeX source documents created a "DVI file", device-independent file, from which postscript files were usually created, although there were DVI readers also. Nowadays, the usual output is PDFs. Further, although years ago it would take several minutes to re-run the typesetting after making changes in the TeX source, nowadays re-typesetting a 30-page document takes an imperceptible time, perhaps a second or two at most. And there are of course various ways of packaging the re-typesetting (as well as creating the TeX source file) in IDEs and so on.