I saved your vids and played them in super-slowmo for a closer look. In the first clip, your takeoff leg bends too much after you leave the ground and it stays bent at about 90-110 degrees all the way through the swing right up until you extend your legs up the pole. That's a problem because by bending your knee, you shorten the length of your leg swinging as a pendulum, putting less energy into the pole. The tradeoff is that you swing up to vertical faster, but you do so having put less energy into the vault.
That said, in the second clip you fixed the problem entirely--you completely extended your takeoff leg, got a big prestretch of your hip/core muscles (your hip flexors are ridiculously mobile) then immediately kickwhipped forwards and upwards with no bend in the knee. The effect of this more forceful swing is that you mushed the pole so that it was recoiling past vertical, leaving you without enough time to extend straight upwards (a good thing--this means you should move to a stiffer pole which will give you more pop off the top). Remember, the key to remember when bending your swing leg is that you should only bend it just as much as needed to get to vertical--bend more to swing faster but weaker, bend less to swing slower but more forcefully. This is something that you shouldn't need to think about--it's something that you'll correct for by feeling.
Your top phases (extending your hips then pulling/pushing off the top of the pole with your arms) are very controlled and neat, especially for someone who's only been jumping for a year. Based on this, your rubber hip flexors and small stature I'm going to go out on a limb and guess that you have a background in gymnastics or something similar. This will help you in everything you do off the ground, but it's the runway where your biggest current problems are, and they are present in both clips.
First, lift your knees higher when you run. Speed is directly related to how quickly and forcefully your hip flexors fire your knees up as your other foot strikes the ground. Think about running with your feet in front of you, like you would when you do "running Bs" as part of warm ups.
Second, carry your pole at a higher angle. Since the pole is low right now, you have to put too much effort into carrying it. This makes it hard to jump with much upward force once you hit takeoff. Start with the pole raised a little higher and lower it in a smooth, controlled drop over your last 3 steps. Some positions to help queue you: 6 steps out the pole should be at about a 60 degree angle with the ground, 3 steps out it should be 30 degrees, when your penultimate foot hits the ground your top hand should be above your shoulder, and before your takeoff foot hits the ground it should be straight above your head. 6-step walking/jogging/running plant drills can help this.
Third, build the cadence of your runway so that your steps get progressively faster. There is a noticeable change between your first 4 and last 6 steps (which is good) but your last six should continue to quicken up--particularly the last two. When I watch videos of elite vaulters and I count their steps, I often find I only count 17 or 19 the first time because I miss their last step since it happens so fast--this is how quick it needs to be! To enforce this, when you do anything with a pole in your hand, even planting drills, practice this cadence too.
Finally, although it's hard to tell because the mat's in the way, you appear to be a touch inside (i.e. the pole is beginning to bend before you have completely left the ground). Remember, any bend in the pole before takeoff is wasted--it takes force out of your jump and redirects it at a lower angle. Part of the reason for this is probably due to the previous two problems, but a good way to get the feel for a free takeoff is with the "pre jump" drill Altius describes here:
http://polevaultpower.com/forum/viewtop ... 8770#98770
Good luck!