You can’t really test for fertility. I mean, I guess you could, with extensive, $$$ testing of some kind. But generally you don’t do that.
You would do a culture and cytology (both, not just one or the other) to determine the cleanliness of the uterine environment, so you don’t go trying to breed into something that isn’t healthy enough to either conceive, or maintain a pregnancy.
You’d do that maybe a month before your earliest intended breeding time, to give you time to clean things up if needed (antibiotics, more diagnostics, etc), but not so long that you risk having another infection develop.
And yes, the FFS test (no longer WFFS since it’s found in non-WB breeds) is a hair DNA test