Let’s try to answer your questions:
- If you’re an Australian citizen, you can fly to Canada. You will have a little trouble at the port of entry, explaining why you left, but you are technically a permanent resident so they should let you in. (Bring a copy of your record of landing!)
- If you need a visa to travel to Canada without PR status then, yes, you need a Permanent Resident Card Travel Document. You can learn more about it here.
- How long it takes to issue depends on the office where you apply for it. You’ll have to contact the High Commission in Canberra.
- No, you are a Permanent Resident. The LMIA requirement is for job offers for foreign workers.