My waters broke at 37+6 with DD1 and I didn't go into labour until at least 12 hours later, ending up with a c/s due to foetal distress. DD2 I went into labour at 39+4 and it was quick, I was 5cm within 3 hours (ended up with another c/s though). So you may not be earlier with #2 but you may also be quicker if you do go spontaneously!

I would voice your concerns with your OB but I would also look at options of staying closer to Melbourne from 37 weeks if possible, just in case.