Here's the best I can make of it. The diarist departs from the system of shorthand in Lewis's textbook in a small number of minor ways. This has not been too much of a problem except that his system of numerals is completely different. I have abandonned the task of working them out, although slightly more detail can be guessed at than I give here. The proper names were a real pain, as the shorthand is a quasi-phonetic system, and little remains of any original spelling. With the help of Google I have identified all the place names as being in and around Adelaide and Adelaide Hills. I was even able to corroborate the landlord Hawkins and his pub, Crafer's (
http://www.southaustralianhistory.com.au/aldgate.htm). The mystery longhand word on page 1 line 15 is `cooeing', that is, `shouting cooee!', a fine Australian word. Here's the transcription, line by line. In pedantic academic style the first page is 1v. (1 verso) and the second is 2r. (2 recto). Uncertain, but likely, readings are in <angle brackets>. Unknown numerals are <?>. Sense breaks down in only a couple of places, marked (sic.)
1v.01 Saturday December <?>. Left the Port with Joe Brown by the <?> train
1v.02 but on reaching town found the omnibus would not leave until half
1v.03 past <?> so wandered about town and went to the Botanic Gardens
1v.04 then to Aldridge's where we had dinner. We then
1v.05 went by the Mount Barker Mail to Crafer's. Brutal driver
1v.06 beat the off wheel-horse under <pretense> that it would not go
1v.07 but it seemed to me he did it only out of spite. Left the
1v.08 ill-used horse at the mountain hut. Passengers had to
1v.09 <walk> up hill. Arrived at Crafer's about <?>. Had
1v.10 tea about 1/<?> past <?>. After tea when it was dark
1v.11 heard a great noise when shortly the landlord arrived in a great
1v.12 passion with a kicking horse which he <calls Raruy (sic.)>. He had
1v.13 been to town about some law affair <concerning> the lease of the
1v.14 house. A family affair. Was in a great passion because
1v.15 he had been cooee-ing a mile off and nobody had heard
1v.16 him. Brown and I slept in a double bedded room.
1v.17 Sunday <?>. Rained all the morning too and we had not
1v.18 got out. Landlord (Mr. Hawkins) cut his
1v.19 forehead open with a stirrup-iron which has
1v.20 not improved his temper. In the afternoon
2r.01 we went through the hills to Mr. Samuel's, supposed to be <?>
2r.02 miles off but we lost our way and must have
2r.03 gone <?> or <?> miles over hill and gully as
2r.04 it took us more than <?> hours and a 1/<?>.
2r.05 Samuel <came> back with us part of the way and we got
2r.06 back to Crafer's in 1 1/<?> hours. Nearly let out (sic.)
2r.07 <?>. <______> rained all the morning and we having no
2r.08 great-coats could not return to town by the
2r.09 Mail as there was only room outside.
2r.10 In the afternoon went to Cox's Creek to the Bridge
2r.11 Water Hotel Mrs. Robinson
2r.12 and (sic.) agreed to send wife and family up, Brown also
2r.13 to send his wife and family. The landlady a
2r.14 buxom dame and jolly woman
That's it! Hope this was useful

Cheers
S.