provide everything you can hun - the more supporting documentation the better it is for you. basically, they will take into account your current situation and will base it on that, so the more they have to base this on, the more likely it is to be passed. the child care centre can also provide additional "support" for your case if needed.

everything you've listed is stuff i would suggest you supply to support you - so you're on the right track. i think a letter from either your GP or oncologist would carry the same weight...

don't include anything about the LWOP situation - it's irrelevant to your current situation and your need for care. i would state that you aren't working and have limited income, but not the reasoning behind why. the assumption would be there that it is related to your illness.

from memory your partner is in the defence force - if he is currently deployed, put in that you have a lack of support due to his employment situation as well...