Your Dr would need to provide a medical certitficate stating that you are unfit for work due to your medical condition. You don't need a medical certificate for any length of time prior. To get Sickness Allowance you need to have a job to return to otherwise your would be looking at Newstart Incapacitated.

You need to take into account that your partners income will effect your entitlement. Actually looking at your situation you would probably be better off claiming Parenting Paymnet Partnered as you wouldn't be required to lodge medical certificates all the time. Again this is all dependant on what your partner earns as to what you would be entitled too.