I think I understand where you are coming from, OP. (aka orginal poster, just if you didn't know--took me awhile to figure that out on here)
First- There is a small little pony at my barn who is 13.2 and jumps like no other. He loves it. Just point him at a jump and off he goes. Moreso he is actually quite a skilled little guy. His current rider jumps him 2'3-2'6 and he does just fine. He has short legs too so I would say there is no doubt that your mare is definetly capable of jumping. Just how high is yet to be determined.
Second- I own a full blooded Arab. It took months and months of really consistant work to get her canter perfect. Your mare sounds just like her. There are a few things you can do to slow down a canter on the flat. First, just for right now, forget jumping and work on slowing her down. What you can do is take her in circles-lots and lots of circles! Doing sprials helps alot too: start out with a large circle about half the size of the arena. Pick a spot on the ground or even put a cone in the middle and slowly take her in smaller and smaller circles getting closer and closer to the cone. Then spiral back out, going away from the cone. The smaller the circles are, the slower she will canter. You can also try stopping and backing her up if she is fast. And I don't mean 2-4 steps. I mean like 10-15 steps back and then stop and "rest" for a minute. Then ask for the canter again.
Now as far as jumping goes: First teach her to jump if she doesn't already know how. I'd try doing trot poles riding her and lunging her over very small jumps, maybe about 10" at first. Once she gets good at that you can raise it up. Never try jumping her with a rider until you can go over a ground pole in all directions at the canter. This is why her canter is very important. Fix that issue first. Then, once you've mastered that, try trotting a small jump, like an 18" cross rail. ALWAYS trot the jumps first with a green jumper. Let her find her footing and build confidence.
Since cross country is always over solid jumps, start taking her over those on the line. At my barn we happen to have barrels and hay bales and a handmade coop to jump so I took my mare on the line and asked her to go over them several times both directions before I tried riding her over it.
If you have any more questions I'd be happy to help. Eveything you are going through is exactly what I just finished dealing with with my Arab. :) So I've been there!!