Hi wella2go, Based upon your explanation I assume that you have two different and unrelated tickets. One ticket is with Singapore Air for your flight between Sydney and Istanbul. The second ticket is with Uzbekistan Airways for your flight between Istanbul and Tashkent. If this is correct there is virtually no way your luggage can be tagged all the way to your final destination. Singapore Air cannot tag your luggage for a flight over which they have no control. Uzbekistan Airways would be in the same position if there even is a representative of Uzbekistan Airways in Sydney.
As far as both of your airlines are concerned you are making two trips. One trip is going to leave you at Istanbul, and the other will leave you at Tashkent.
So, when you arrive you must leave the plane, get a visa, pass through immigration, leave the secure area of the airport and collect your luggage, pass through security with your luggage, check your luggage in with Uzbekistan Airways, go through a second security check and make your way to the gate of your flight with Uzbekistan. If you have not printed your boarding pass for the Uzbekistan flight you will also have to get that while you are checking in your luggage.
I think most people would be comfortable with a two and one-half hour transfer time. If your plane is on time and the lines for visa and immigration are not exceptionally long you should not have much difficulty. You might purchase an evisa which would speed up the process a bit. I do not think you will have lots of spare time, so I would get my luggage checked in and pass through security before I stopped for a meal or any other activity.