9 months isn't long. I'll be at 2 years in July, still feel very much like a beginner, and I hope I still have a lot of room for improvement. I've heard that progression varies greatly by person, but it seems that 3 years is pretty average to get a lot of the physiological changes in place.
That said, I started to see pretty dramatic improvments after 9 months, but I also started training with a power meter around that time.
This year, the biggest change I've noticed is my ability to recover quickly during a ride. I used to be 'done' after a hard effort, now I'm ready for more after backing off or sitting in for a couple minutes.
When I started out, averaging 16.5 mph was pretty good for me. Withing 9 months, 18 was reasonable. I can average over 20 now, but mph isn't really a good metric unless you are doing TT's. You'll quickly learn that a 20mph group ride can be much, much harder than a 22mph ride, it just depends on who is pushing the pace and when.
One thing you need in cycling is patience. Genetics are also good. You might try reading Joe Friel's "Training Bible". It's really written for a racer in mind, but you can learn a lot about the physiology of cycling if you are into that sort of thing.