Forgive me if I'm wrong but doesn't the baby have to be born before the payments can start?
So in a sense if your employer does what the promised they can be up to 10 weeks of your pay out of pocket (4 weeks before due date, possible 2 weeks over due and possibly 4 weeks for centre link to process money to them)
Yes that's right, but your employer can pay you before they receive the CL lump sum for your PPL. It's at their discretion I believe.

I haven't heard of any company that would commence payments before a baby was born.

I would definitely not be relying on this to happen, with out talking to whomever does your payroll - and understanding what their directive is.

I think you need to be looking at other ways of budgeting / finding the money.

Can your husband not get any more hours, either where is, or somewhere else?
Even casually somewhere - nightfill at a local supermarket?
A friend of mine worked at Coles and her PPL payments started the week after she finished up. Trouble with DH job is he will get a txt that morning saying if there is no work, so it's very frustrating. He has no licence until end of July so we are kind of stuck until then. I have been doing everything in my power to save, but have had to use my 'baby' savings twice already for rent and bond ( we just moved house) so have 1/3 of what I estimated to have saved.

Hmmm, I will definitely call CL when I get a chance. They might be able to help.