WOW! Great transition to the canter!
I like how you are quiet with your hands, your horse was willing to go forward because of your leg. Looks like an honest horse, so if he feels ready to take it to the next level, go for it!
What I recommend before jumping:
Contact is Crucial!
While approaching a jump you must stay steady, let the horse keep a steady forward rhythm.
Just before the jump (breatheeee, exhale!) you will advance properly when your horse knows where his feet are.
Over the jump you don't want to change a thing (unless you're jumpers, it gets in depth hah).
--- Now to achieve a steady pace and keep contact after the jump, I recommend starting with ground poles and caveletti's. These can really help the rider and the horse allow each other to move in sync. While approaching an elevated pole (caveletti) let your horse accept the bit. Push him forward (not faster!) and really allow him the rein to take the bit. Keep the forward motion and your contact on the rein and maybe throw in circles and serpentine's.
I know I ramble, but you are only a few steps away from being really ready to jump.
It's all about flatwork. Really take your time to get in touch with your horses bending, extending, and praise!
Here's a reference video I've found....