Hi im a permenent resident and been here 2 months, my partner is a temporary resident been sponsored by myself on a partner visa, are we eligable to buy a property? or does she have to have PR?

You, as a PR, can buy a house with no need for approval, however it seems that if you wanted to buy jointly that your partner may need FIRB approval as she's not married to an Australian citizen.

i dont believe you have to be a PR to buy property, hence overseas investors.

You do have to be a PR to get a mortgage though, so it might need to go in your name only. Check with bank. Also you will have to pass a credit check, which may get initially declined if you've only been here a very short time.

Also if one of you is a PR (which you are) and you have never owned any Australian property, you may be eligible for the the first home owners grant and possible stamp duty concessions

You don't both need to be PR to get a mortgage, my partner and I have one and he is on a special category temporary visa (as the defacto spouse of an NZ citizen). I am also technically not PR, but again on a special category visa as an NZ citizen. We have an ANZ mortgage and had no issues getting it.

We did have to get FIRB approval for him to buy the house, and yes we got first home owner's grant.