I would wager that your feet come out of your stirrups at a canter because you are behind the movement of the horse - ie you have a "chair seat," where your legs come forward, out from under your hip/shoulder/ear alignment, putting you into a "chair" position.
Never fear! This is a common occurence, even in some very experienced riders! Adjusting to different horses is not always easy, and undoubtedly, you might find yourself behind the horse's motion at times.
To resolve this, practice keeping your heel aligned with your hip, which should be in line with your shoulder and ear. If you could draw a line from your ear straight down, the line would pass through your shoulder, your hip, and your heel.
Keeping your toes up (as opposed to thinking "heels down," which can sometimes be troublesome) will help you secure your seat and keep you balanced.
A good image, in my opinion, to think of for a correct seat, is to imagine yourself positioned so that if your horse were to simply vanish from under you, you would not fall down on your bum or alternatively on your face, but land on your feet, with your knees slightly bent. Practice sitting on your horse and having someone check your alignment; it might feel unnatural at first to change your leg position or even where you are sitting in the saddle, but soon it becomes muscle memory.
Keep us updated on how you are progressing into a more solid seat in the near future!