I'm 35 and have a 9cm fluid-filled ovarian cyst that has not resolved in 6+ months. Doc wants to remove that ovary. Is this the best treatment?

Yes. A cyst that has not resolved in 6 months is abnormal. A cyst that is 9 cm across is very abnormal. Removal is really the only option, other than doing nothing.
No keep ovary. You still requier surgery but you can have just the cyst removed. It should be done laparascopicaly to minimize your risks and allow for faster recovery.