Hey Honeybun. There are a few key things you are doing very well for beginning jumping. The first is getting into your two-point a few strides before the fence (which may be misconstrued on here as jumping ahead or trying to jump for your horse). It is clear that you are getting into your position and allowing the horse to take the jump. This is a great first step when learning to jump. The second good thing that you are doing is grabbing some mane over the fence. Since you are still just learning and need to strengthen your position, this will keep you from catching your horse in the mouth or landing on his back.
That being said, there are two key things you need to work on; important things to focus on first. The first is your hands. They look very stiff as you are trotting towards the fence, which is annoying your horse a bit. You really need to learn to relax through your elbows and allow your hands to follow your horse's movement. This is going to be very important for you to progress as a rider, not just for jumping.
The second key area you should focus on is strengthening your leg position.I can see your legs sliding around in the saddle over the fence. You should have contact with your horse's side through your inner thigh, knee and calf, with most of the pressure in your thigh and calf. Your leg should lock and stay right behind the girth over the fence, without sliding backward and forward. To strengthen your leg position, raise your stirrups a hole and ride lots and lots and lots (did I say lots?) of two-point--especially at a trot. Be sure that you aren't supporting your weight with your hands. Stay in two-point 10 times around the ring or longer, not just for a few seconds. Stay in two-point until you are so tired and your ankles hurt so much that you think you are going to fall off.
This will teach you better balance and allow you to support yourself with your legs, as well as strengthening your muscles.
Also, if you could get some tall boots or half chaps, that would really help give you some added stick.
Hope this helps!