Just
looking around a bit, while you are eligible to apply for a visa it will most likely be granted for either a one or three year period (of course, renewals are possible and you could later try for permanent resident status).
You have a few paperwork hurdles to jump in order to prove your status. The documents are listed under
#2 in the link.
Of course, for current and authoritative information, check the actual official Immigration website.
The great thing about your visa status would be that there are practically no restrictions on the type of work you can try to get.