You can not apply for a US Visa from within the US - it needs to be done outside of the country. In general the best place to apply is in her home country (Australia, I presume). It's also possible to apply via the US consulate at any other country, however it may take longer for the application to be processed, and there may be a higher chance of being denied - depending on the specific circumstances.
Taking a short trip to Canada or Mexico will NOT extend the 90 day allowable period for the Visa Waiver Program (VWP/ESTA), and in fact any time spent in Canada or Mexico will count against the 90 days allowed under the VWP.
Taking a short trip to another country (eg, somewhere in Europe) will technically reset the 90 day period, however there is at least a chance that re-entry to the US will be denied if the immigration officer believes that the purpose of the trip to Europe was simply to extend the time spent in the US. There are some comments on that situation in the answer to this question - How soon can I re-enter the US after my previous visit?