It does sound like the landlad is unaware that the fridge is yours. I find it unsual that she is renting rooms and not providing a fridge of her own for the flat. I fear that if you don't resolve this with your landlord before the new person moves in they will react badly. I urge you to let her know this is your property as soon as possible, definitely before she shows the room to anyone. I would expect that a stove and fridge are provided if I was renting a flat, but microwave, cutlery and table would not be. I did some searching to see if it was required to provide a fridge/stove, but it appears not according to this:
https://www.commerce.wa.gov.au/sites...nantsguide.pdf

She cannot compel you to share what is yours with the new tenant, but being overly possessive won't win you any friends. If your fridge is half empty anyway, it will run better if their food is in there too.