Given that words like "spa" and "bra" generate intrusive /r/, it doesn't seem like much of a stretch to analyse "father" as /farðə/. In fact analysing BAD as TRAP + /r/ would neaten up the vowel system a lot, there's just no evidence in the form of intrusive /r/ for it.
Of course there's other problems in analysing AusEng as such; namely the merry/Mary distinction, which you'd have to analyse as /merəj/ ~ /merrəj/.
Apart from this, it works surprisingly well. Stressed syllables can be analysed as obligatorily /i ʊ e ɵ æ a ɒ/ + consonant and unstressed syllables as /ə/ + consonant. Long vowels are V + r (except /ɒ/ can't be followed by /r[C,#]/, and /ɵ/ must be followed by /r[C,#]/, so if you were very keen you could analyse them both as allophones of /ɔ/). Diphthongs you could probably call /ij ʊw æj aw aj æw/ (size=80]FLEECE GOOSE FACE GOAT PRICE MOUTH[/size]). Unstressed syllables get schwa plus /əj əw ər əl ən/ = happY follOW commA/lettER bottLE happEN. Thus I can claim that AusEng is a VC language rather than a CV one. It's genuinely not a bad analysis.