Can you ask for a leave of absence or something like that?
Not sure what you do (and at what level) or how valued you are by your employer, but it's possible they might rather have a trial w/o you than a scenario in which you just leave outright. The advantage for them is that it will be planned, so you can probably work to train your temporary replacement, and then they can boot the temp if you want to come back, or leave the temp on so BAU can continue until they find a permanent replacement if you decide you want to leave.
And yes, like others have stated you can't use FMLA unless it's a newborn, or a newly adopted child (or perhaps a newly fostered child?), or you need to care for an ill family member or yourself.