I am not sure if you are using all the tools, Moz offers but here is something I looked at and took 5 minutes.
I used one of your keywords that you want to rank for - furniture movers melbourne
I then took from the SERP Analysis, the top two websites.
Then in the keyword analysis, I used your website domain and did entire root. THen added two of your competitor's websites. You will see all the keywords everyone ranks for. When you go to their websites, it seems they have a lot more content than you. Maybe start adding more content about the services built around your keywords.
