I agree.This might not be an opinion that you like and I promise I mean this in a caring way - maybe now is not the right time for you to buy?
If you're saving $650 a fortnight without paying rent, but having to tap into this for emergency expenses (which will always come up, including when you have a mortgage), then you need to consider if you could afford the repayments at the moment, even if you did have the deposit? I'm not sure what sort of price range you're looking at but when you factor in all the extra costs that come along with home ownership, along with putting a bit aside for those emergency expenses to allow you to still pay the mortgage if they did come up - it sounds like you'd be able to afford to pay a max of about $200 - $250 a week in repayments.
Houses are expensive - you have to factor in rates, insurance, maintenance (what if you needed a new roof for example?) and you don't want to get yourself into a precarious financial situation by absolutely stretching yourself with the repayments.
The other thing to consider when looking at if you can afford the repayments is the fact that interest rates are at an all time low and will likely go up in the life of your mortgage, so you need to be able to pay more than the minimum payment on these interest rates.
Sorry to be a Debbie Downer. Xx
Also if your wanting to have another baby.