How to ask for a permanent position?

I have been working for a company for 3 months as a temp and they said they would make me permanent if i am good ect.

however over the weeks we got talking and i told them i am going uni next September which i know i shouldn't have as now there is a permanent position available and another girl who started after me has been told by the manager to apply for it.
I no they told her and not me as they said you are going soon but the thing is September is far away!

anyway the reason i want a permanent position is because I am planning on buying a house next year with my other half and wont be able to get a mortgage if i don't have a permanent job.

Should I ask my manger if I can apply for the permanent position too, should i say anything about buying a house or not? Not sure if that's silly.
by the way i am a good worker, always on time ect and meet my goals

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