Cover letter when looking for sponsorship (Sydney)

Hi all,

I would like to move to Australia for work in the computer animation industry, and have begun the process of researching companies that I would like to work for. However, I do not have a work visa, so I assume the only way to get a job is to get sponsored by a company..

So I have a few questions:

First, when applying for jobs (or even just emailing companies that don't currently have job openings), what is the best way to phrase in a cover letter that I am not able to work unless I am sponsored? Is this something that should even be brought up in a cover letter, or wait until I get a response from a company?

Secondly, I am heading down to Australia for a short vacation in the next few weeks. Would it be better to just wait until I am down there, and then email companies telling them that I am in the country, and would be available to meet.

Lastly, is there more likelihood of getting a job if I have an Australia telephone number? Should I get a temporary sim card when down in Australia, so I can have that number available on my resume?

Thanks for any help,
Adam