I'd meet with your new dr first as he may want to do new tests anyway (some just do!). Then if you are happy with him and want to move clinics for sure, then just request your nurse or receptionist to make a copy of any tests and results you had taken with them. If you ask nicely they may not charge you, but they may. Not sure if it would be Medicare claimable though as it will be an admin fee.

And absolutely you can move your embryo if you new clinic agree to transfer it. There would be charges with respect to this and I would ask if there are Medicare Item numbers for the fee so you can see if you can get any funds back. I've no idea how much they would charge.

I also wanted to mention that it used to be (back when I did IVF from 2007-2010) that the average number of cycles it took to fall pregnant through assisted conception was about 7. Not sure if the odds have improved over the last few years though with improved technology. Sometimes persistence and multiple transfers is the only thing that pays off.