No Sir.
Under FAR Pt 61 a BFR (BiAnnual Flight Review) is done by a CFI
Specifically FAR 61.56
(a) Except as provided in paragraphs (b) and (f) of this section, a flight review consists of a minimum of 1 hour of flight training and 1 hour of ground training. The review must include:
(1) A review of the current general operating and flight rules of part 91 of this chapter; and
(2) A review of those maneuvers and procedures that, at the discretion of the person giving the review, are necessary for the pilot to demonstrate the safe exercise of the privileges of the pilot certificate.
(b) Glider pilots may substitute a minimum of three instructional flights in a glider, each of which includes a flight to traffic pattern altitude, in lieu of the 1 hour of flight training required in paragraph (a) of this section.
(c) Except as provided in paragraphs (d), (e), and (g) of this section, no person may act as pilot in command of an aircraft unless, since the beginning of the 24th calendar month before the month in which that pilot acts as pilot in command, that person has—
(1) Accomplished a flight review given in an aircraft for which that pilot is rated by an authorized instructor and
(2) A logbook endorsed from an authorized instructor who gave the review certifying that the person has satisfactorily completed the review.
To clarify and not have to quote the complete set of regulations lest you think I deleted or omitted something
Subpart (d) refers to taking a checkride with an examiner and points out that if you have passed a ride you do not need a BFR as the pilot certificate, rating, or operating privilege checkride counts as a BFR
Subpart (e) refers to participation in the FAA Wings program
Subpart (g) refers to student pilots undergoing training. Obviously if your training and have a current solo endorsement.....BFR need not apply.
I'd suggest to you that you review the FARS as they are available online.
If you still believe you need a DPE please consider:
To Serve Outside the United States (U.S.). A designee may be appointed to serve outside the United States provided there is a demonstrated need that such designation will serve U.S. citizens abroad and an FAA office can properly supervise the designee’s activities. The designee is subject to limitations as provided by current FAA policy regarding the certification of airmen outside the United States.
Pretty tough to find one in Australia as a Designee needs approval to work outside his region.
To my knowlege there is no designee in Australia.