Sounds like the cat may be too big to be ducking under the gate, this works with one of mine but she's only 2.5kilos or so. Cody picked up the cat flap idea fairly quickly too from watching the cats which is just as well because we have them in several of our internal door also
Another option is to put the litterbox on a table top out of the dogs reach.
One of my cats had great difficulty getting to grips with jumping the gate because the gate was to thin for him to balance on top of, it took almost 2 weeks until he was managing it ! This is the same cat who has no problem clearing a 7ft fence in the garden when he gets the chance or escaping out of the skylights upstairs
Stephen 3 Cavs - Cody, Abigail & Jasmine, Gavin the terrier and the cats - Buffy, Kendra, Thomas, Caleb, Robin & Cadbury, the Geckos - Crane, Poole, Schmidt, Amber, Seven, Eleven, Thirteen, Ivy, Gretchen, Darcy, Ari, Zeva, Claude & Claudine, Alpha, Bravo, Charlie, Delta, Dov, Ronia, Netanya