How come you only found out today? Your teacher should have known six weeks ago. You would have paid two months ago, too. Not a good idea to prepare last minute for an exam, but I wish you well with it.
If you still work on the Kabalevsky, work on short sections of a couple of bars and go over them ten or twenty times in a row. Start with a larger drop forward from the wrists and work towards a faster speed with small, quick wrist movements. Once you have direct accuracy, the speed should increase automatically. Focus on using the wrist and make sure you are not using the lower arm. Quickly get into the keys and out again. (A quick tap) Use your lower arm to move your fingers over the keys sideways instead of trying to move across the keys using your fingers. Make sure you lift well and don't get 'stuck' in the keys for a moment.
It is not a long or complicated piece so you should have time to get this done if you focus on small sections.
With the AMEB at grade 4, variety of programme is not an issue. Both Tanets and Melody are list A, so that should not be a reason for not playing it.
However, Melody is almost as fast as Tanets and is nearly all played with the left hand and requires maturity of expression. Musically, Tanets is a far easier piece.
Take your teacher's advice, though.
About not panicking - proper preparation is really the best way. However, you have made a decision about how you have used your time - just work with full concentration as much as possible over the next few days. Give it everything you have got. An exam is not the end of the world - if you don't pass, you still can move forward in your grades and pieces. The reason for exams at your level is to learn how to manage the demands of structured practice / performance preparation and to receive a reward for your efforts.
Topic: Exam!