The problem is how word processors are generally designed. If a word doesn't exist in the dictionary the word processor will offer suggestions. One suggestion is, if the word can be broken into two words separated by a space, then the two single words are suggested.
In Microsoft Office the word "coathanger" is not present and thus "coat hanger" is suggested, which is not correct according to the leading authoritative dictionary resources used in Australia. A similar situation exists for the word "spellcheck" where "spell check" which is not correct is suggested. People often become so used to the misspelling they end up believing it is the correct spelling.
When I found this issue I had to double check both the Oxford and Macquarie dictionaries, and both include the spelling "coathanger".
If you check Australian usage using Search Australia, you'll find approximately 4,000 occurrences of "coathanger" and approximately 13,000 occurrences of "coat hanger". This is a staggeringly high percentage of people incorrectly spelling the word and shows just how dependent we are on our word processors.
The preferred Australian English spelling files for Microsoft Office and Internet Explorer will soon fix this issue as well as thousands of other existing issues with the Microsoft spellchecker.
It is possible that both the Oxford and Macquarie dictionaries are wrong and the Microsoft Office spellchecker is correct. This however is unlikely.