I think that one specific hair color won't make every person who dyes their hair that color look older. It depends on the exact person, face shape, coloring (skin and natural hair, etc), and really can't be generalized. A picture would be helpful, but it's fine if you can't/don't want to post one.
That said, let me see what kind of advice I can give. It sounds like she's in for some change, which I completely understand because I just made major changes myself.
I suggest that you go to a salon rather than using a dye kit and doing it yourself. You will pay more, but that in itself will make you look far more mature than the kind of flat, one-color dye jobs or bad do-it-yourself highlights that many 14-year-olds get. If the money is a problem, you might want to ask for a salon trip as a birthday gift or do some extra babysitting, but it's worth it.
How is her hair now? If it's all one length, adding layers or something subtle like that will immediately look better and more grown-up. If she wants a more dramatic change, she should as the stylist for advice about what length and cut would best suit her.
As for the color, I suggest very subtle highlights--not necessarily giant streaks of bleach-blonde, but small streaks just a few shades lighter than her normal coloring. My friend has medium brown hair and her highlights are a goldeny-light brown color that blends very well with her hair. Her cut is a classic layered cut and she looks gorgeous. I have dark blonde/light brown hair and I just cut it very short and added blonde highlights mixed in. Mine are a bit more dramatic than hers because the whole look is funkier, but we are both mistaken for 18-20 years old and we're 16. Oh, and I knew that I could do the blonde because my hair was very very blonde when I was little, so the color suits me. If your hair has gotten darker as you've gotten older, you can look to your hair color when you were little to see what will suit you best...so if you've always had dark brown hair, don't bleach it just because you can. Ew.
One more thing about color--you can go lighter than your hair color, but not darker. Light roots look weird. If you change colors--say, from brown to red--you should stay at the same level of darkness/lightness and just change the hue. You
could go for a lighter shade of red than your brown hair, but not darker. Does that make sense?
Also, if you want to look older (I say you and not her because, well, she's right there so she's reading too), a very small amount of makeup can help. Too much will make you look like a little girl playing dressup or a wh*re, so don't dump it on. You're young, so you really shouldn't wear a lot or you'll look funny in it. No lipstick--you're too young. No glitter--it's tacky and you'll look younger. No rings of liquid eyeliner--it's tacky and you'll look terrible. No rings of blue eyeshadow--it's tacky (unless you reeeeaally know what you're doing) and it's usually a very middle school look. I don't know whether you wear anything now, but I suggest just a bit of mascara and some (tinted?) lip gloss/balm. If you want some cheap lip stuff, lots of people here suggest lipsmackers for winter (dr pepper for a light tint, certain others for just some shine). They smell good, too. I'm actually going to pick some up this weekend because they're great for winter.
If you want more high-brow kinds of things, I'm sure that you can find plenty of recommendations here. Lancome juicy tubes and MAC lipglass are great, but they'll cost a lot.
Good luck.
Tell us what you choose.
Edit: Woah, I wrote a
ton. Um, I hope it helps!
I also see typos, but I'm just too lazy...
shes hear for new years still)hazel eyes. i told her that i cant tell what makes her look a bit older since i have no clue? 
