These days converting from AME to LAME is becoming non existent. The major airlines generally have enough and are actually downsizing numbers. (Virgin actually have LAME's employed as AME's and employ vacancy control.) So, with their existing LAMEs, their isn't much need to train anyone on new types. With regards to QF Perth, I suspect what the local management originally told the current AME's regarding being trained up to LAME will not transpire. They keep talking about getting a hangar in Perth and most AME's will be used there.
Coming from the military will probably put you at the bottom of the list behind current employed AME's thats assuming you even get in the door. Sorry to be so negative but thats the way things are headed. LAME's whilst being highly trained are considered expensive by airline management and therefore they are all about limiting numbers.