Should I break up?

I am a 20 year old male and I've been in my first relationship for 9 months now with my girlfriend who's just about to turn 16. I love her very much and the best thing I know, is to spend my time together with her.

However, I feel our relationship is starting to have quite a few problems:

- First of all, there is the obvious age difference. However, she is somewhat mature and none of our friends/families have any problems with it, so this is the least of our problems.

- She haven't had a phone and her internet at home sucks, which makes her impossible to reach.

- While I often partake in things I don't personally really like (like drawing) I often feel it's difficult to make her try things I want to do.

- She likes to sleep till 4 pm and she doesn't want sex nearly as often as I do

- She's indecisive, irresponsible and awful to make plans with.

- I've said these things to her countless of times, but I don't see much change in the way things are.

I love her as much as ever and she often makes up for these mistakes, by being very sweet and caring. But something inside me tells me, that I could do better. That I should give her up and find someone who is more responsible (and with a little more sexdrive). It's just that, despite all her faults, I still very much love her and if I break up with her, I'll have no one to cuddle with, no one to direct all my love towards, noone to do a playthrough of Zelda: Ocarina of Time with and no one to hold hands and talk with...