Hi Jeff
Yes, what you are proposing is possible. Though other alternatives are open for you to consider.
Do you know whether you are eligible for a First Home - New Home Grant?
First Home - New Home scheme | Office of State Revenue
If you went ahead with your proposed purchase of this existing house, you would loose your entitlement to the First Home - New Home Grant (if you are eligible)...
If your father will own half of this property debt free, and is willing to provide a guarantee, and security to a bank to support your purchase of a Property... you might be able to purchase any new (and take advantage of the First Home - New Home Grant) or existing property 100% in your name, with this support (if it is required, and you could not obtain a loan without such support).
As a twist you might be able to purchase 100% of this existing property, and pay out your Dad as well as your uncle.
Who is the Executor nominated by the Will? Have you run your proposal by them?
If you buy a property, and you have a co-owner, even if it is your Dad... I would recommend a co-ownership agreement which would set out how everything would work in advance, so the possibility of a dispute is reduced.
I await your responses, kind regards, James