Just changed employer - of course you just sign after you receive a signed contract from the new employer. Everything else is, let's say it nicely, risky.
When I joined QR I had no such letter. Only thing I had was a reference letter from my previous employer and having that must not mean that you resigned.
If I would have a choice with ANY ME carrier I would just ask for long term unpaid leave and then see if it is really for you.
I know that there are pilots around down there just being on a kind of leave from their present employer and as soon as they need them again they will head back in their home country. Will not specify that of course.
Best and , IMHO, the only way to do it down there. Have always a backup plan.