Australian English is a non-rhotic dialect, so 'AH' and 'AR' are indistinguishable. It doesn't surprise me that people do write it incorrectly though. I've found that understandings of phonics are absolutely dire even amongst teachers apparently trained to teach it, so people with no experience of/with phonics must really struggle.
If we're talking IPA, cat is kæt, æ being a very short sound not found in a lot of American dialects.
Kari, father, past and cart all contain ä (also written as aː).