On a tourist visa you would be entitled health care under the reciprocal health agreement. However this wouldnt cover you for scans or maternity appointments. It's intended for what is medicaly neccesary ie you go into labour.
He has to tell DIAC of his changed status. Unless he has a condition stating that he sould not marry before entering Australia it should not cause major problems, but they may want to know why you were not mentioned previously in or during his application.
Do you know the conditions of the spouse visa? You have to be in a defacto relationship ie living together as man and wife for a year prior to applying and be able to prove it. Being pregnant in itself wont get you the visa you need to meet the defacto requirements too. If you have been living together for a year or more DIAC may question why you were not added to his visa. It is alos frowned upon by DIAC for you to arrive on a tourist visa with the intention to live in Australia, they can turn you back at immigration if they feel thats what you intend to do, though there are posts in the Migration Issues section of people who have done this. What type of tourist visas will you be going on?
Also, unless you already have one you are going to need a Court Order or signed declaration from your daughters father to take her out of the country to live. This would obviously need to be done in the UK, Australia will not issue you/her with a residence visa without it.
If you meet the criteria for a spouse visa and get the consent for your daughter you may actually be best applying in the UK for you visa. It's quicker than applying in Australia usually and will allow you to get the maternity care you will need. But with so many issues you may be best consulting a Registered Migration Agent, did your partner use one for his visa?