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The Coat of Arms is not the Tassie Coat of Arms, what is the origin of it?

Can you show us an image so we know what you are referring to?
The Tasmanian Coat of Arms was not approved until 1917.Thats the two Tasmanian Tigers version.
I believe but am not certain that the Tasmanian colonial coat of arms is the coat of arms of the United Kingdom - a lion on the left and a unicorn on the right.
Certainly this was used in many Tasmanian Frank stamps and also on the flap or front of much Colonial government stationary. It also appears on Acts of the Tas Colonial Parliament.

It makes sense that the Tasmanian Colonial Government would have to use the symbol of British Authority.

Heres an image from an Exhibition envelop flap. Its looks the same to me as that used on Frank Stamps as well as Acts of Parliament .
"Dieu et mon Droit" appears on the united Kingdom coat of arms as well as the Tasmanian version . Is this what you are talking about?
Can anyone verify this ?

By coincidence I found this catalogue of Coats of Arms used in Frank stamps in Karmans "Frank and Free" catalogue.
while this relates to Frank Stamps the same designs or similar might be found on Tas Postal Stationary, official documents, Acts of Parliament and other official papers.
I am now sure this is the Coat of Arms of the United Kingdom. Close inspection shows the shields of the 4 Kingdoms -England, Ireland, Scotland and Wales.
Pete

The coat or arms appears here