I have never heard of anyone having an issue with getting their QF points credited. Of course, I have never actually
seen anyone try to get QF points credited, so...
From the rental agency end, it all goes into the same spot that any other loyalty programs get put in (it's all automatic from the rental system side--just make sure your number is actually in their system; it doesn't always get transferred over from the reservation system if you entered it on the website), so QF should work just as well as UA, AA, DL, AS, et al.
Also, make sure the name on your rental contract is an exact match with the name on your frequent flyer account. Some airlines vigorously enforce that and will not credit if there's a mismatch.