The rack is pretty low over the tire, but there is still room for fenders. Velo Orange alloy fenders would be very pretty, would require LBS install unless you are reasonably handy with drill, saw, etc. Planet Bike Hardcore or Cascadia fenders would fit and require only a screwdriver and 8 mm/10 mm wrenches. Haven't used SKS Chromoplast.
My wife's rack was installed by the LBS very low, like the OP's but I can adjust them to be much higher off the tire in case she wants fenders. Perhaps the OP should have a look at the installation and see if there is a way to increase the height, that would allow many more fender options.
Pics of the two connections of the rack to the bike (the axle and the connection to the seatstays or seatpost) would help.