I have spoken to Singapore High commission and they have provided me with an email which I can show Singapore Airlines.

The email basically says:

"As long as you do not need to go through. Immigration you will not need to worry .about the passport in the shared transit. area of terminals 1, 2 and 3 in Changi .Airport. You will, however, need to spe.ak to your airline to know whether you c.an check in your seat from Australia."

Singapore Airlines requested a document for me to print off showing this from the Singapore Embassy so hopefully this will be enough for Singapore Airlines to allow me to board my flight!