Yep, they may ask you for a birth cert if your LO looks close to 2 (and they have every right too)

Our DS has flown heaps with us prior to him being 2 - From Adelaide to Perth twice, Gold Coast, Cairns and Melbourne twice. We were only asked for his birth certificate once when he was closer to 2 and looked a bit older.
We are about to go on our first flight since he turned 2 - the the Gold Coast, and frankly I am very glad he has his own seat now, he will happily sit with seat belt on and watch his DVD player, and with paying for an extra fare, you also get more luggage allowance (we had to pay excess luggage on one of our flights - Boo Hoo)

I wouldn't risk it as if they make you pay, there is no guarantee there will be a spare seat on the plane for you to purchase anyway, so it may end up being very costly

I believe there are restraints you can use for LO rather then relying on the standard seat belt, but you would be best checking with your airline