Everything sounds perfectly fine: age, weight, board length, surfing progress, other activities, etc. You have also produced a post that uses proper grammer and spelling that far too many Uni students fail to use when asking similar questions. All in all, you sound like a very well-together teenager.
I learned to surf on a 1-day per week schedule at age 47. At that age, I'd long lost all the fitness that you possess in your little finger. As an adult-learner, I always wished I learned to surf when I was a kid because that is when most things physical are easiest to learn. So, you have that benefit as well.
Your surfing progress is within the average catagory. So, keep the stoke! The wobble you experience is one of the key problems for a beginner. You'd experience less wobble with a longer board (say 8 1/2 ft) or waves that have a little more power in them. I wouldn't bother to get a longer board due to your relatively low weight. But, you might be able to find more powerful waves. They'll push the board harder and make it more stable. But, you'll also have to pop up faster and correctly.
Yes, you should break the knee habit and make a habit of going straight to your feet. I see many women do it with ease, so anyone should be able to do it. Do 2 types of exercises on land to help: 1) push ups (real ones, not the ones on your knees), and 2) squat thrust (http://www.youtube.com/watch?v=rpDRwxR6jHI
). These will help a tremendous amount. You must also ride enough broken waves (white water) so that it becomes instinct to paddle hard, place hands on board, and pop up (no knee). I'll have people I teach to surf do this all day long for 5 to 6 outings. Then when they ride green waves their body knows what to do without thinking about it. Your ultimate goals are 1) to stop wobbling, and 2) catch & stand on green waves every time you want to.
Off-topic: what instruments do you play?