A Medicare card will be okay (which is a card nearly all of us carry in our wallets or purses). - as I've said I/we get out of the cab and walk straight to the gate (often via the Q lounge). A birth certificate shown at the gate carries no more weight on it's own in terms of verification than a m/c card or a print out of the booking.
And I wouldn't be traveling with such a valuable document as a birth cert. anyway. Leave that safe at home.
True, Ron. I take your point