I first cantered about 6 months after I started riding, but I was an older lady. I was not well taught and my opportunities to canter were frustratingly few and far between and that was frustrating.
When you start canter will depend on your RS and how old you are, whether you are having private lessons or are in a group, how often you ride and for how long - so many variables.
However you say OP you have been riding 9 months and can only walk and do a bit of rising trot. You seem to have noticed your progress is slow. I cant comment on your school. But I have seen several of my grandchildren learning to ride.
One local school which teaches masses of beginners has them lead round in a group lesson. But every lesson includes rising trot and sitting trot, once on each rein ( which means circling round clockwise and anticlockwise, once in each direction.)
As soon as children get the hang of rising and sitting trot, they move up into a class where the ponies are not led, and where the students can practice walk and trot, till they are ready to learn canter. They will be balanced in the saddle, able to steer the horse, go easily between halt, walk and trot and be able to trot without stirrups. I would expect someone who has been learning for 9 months to have been given lots of practice in all these things.
If you have a private lesson you are likely to learn faster, but many adults and children pick up rising and sitting trot quite quickly and it is really important to have enough practise. If you are only doing a bit of rising trot, may be you are not getting much practise?