Being in a long distance relationship (dating) is not the same as living together. While you have stated that you are willing to relocate, she has declared that she will not. I think the whole "soul mate" thing is a bit one sided.

I want you to be happy, BUT:

What if you move back to Singapore and things don't go as planned between the two of you? Will you be able to go back to Perth? (visa, etc.)

What if your career is hampered by living in Singapore? Are you able to accept that without feeling resentful towards her?

Moving home also means living with your mom. Can you do that after being on your own? Are you willing to fill your father's shoes?