Shipping company from Miami to Perth?

Hi I really need assistance to find a reliable and affordable shipping company to move my personal effects to Perth. I'm currently in Miami and heading to Perth- Permanent Residency- in December this year. I've been searching for shipping companies and am rather confused by it all. the first offered to ship everything door - to door for 2,000 USD without looking at my shipment (approximately 120 cubic feet), asking me basic questions about my visa, they didn't send me any forms to complete etc.. on further investigation I realised that they were most likely a scam company...reviews mentioned the prices being doubled once the shipment had been delivered. The second company -with great reviews- said they could take my small load in a 200 cubic feet container. This was quoted at 4,000 USD with all of the paper work completed etc...now, my query to them was that as I'm not using 80 cubic feet will my price be lowered? He said no. This is the smallest size shipment that company makes..I really can't afford to send personal effects (books, clothes, souvenirs) for that amount of money. Does anyone know of a good reputable shipping company who can take my shipment to Australia door to door without the worry that I'm being scammed or ripped off... Thank you for your time