Can my employer fire me??

I am very new to the company I work for (since May 7th) and I am all set-up for having WLS surgery the 2nd week of September. Having that I have not been emplyed by the company for 12 months yet I am not eligible for FMLA. I know I will need 4-6 weeks out, and I don't care whether they are paid or un-paid, but my big concern is if my employer can fire me for having the surgery done even though I have not been employed at the company for a long time?? Any info is greatly appreciated!! Thanks

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