Applying for a job when you know you're quitting in 5 months

Hi,

To make things short I'm starting grad school this summer and have around 5-6 months until then to work. I want to work in my field of study as all my work experience so far has been irrelevant. I'm trying to look for temporary/contract jobs but they are hard to come across. What are your thoughts about applying for a full-time job and giving them a 1 month/2 week notice before I have to leave? Rat? Fair?

Thanks

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