There is a saying, "Making it to third base doesn't raise the score any higher than striking out." In other words, there really is no more meaning to oral sex than not having any sexual expression the relationship at all. Ask her why she thinks 14 is too young. Will her mind change so very much in the 24 hour difference between being 14 years 363 days old and 15 years even? What is the true root cause of her apprehension toward sex? After all, you are putting other parts of your body within her (your fingers, your tongue), why not your penis? Besides, she sucks your penis right? You've
already put it inside of her body. Tell her you want to look into her eyes as you do it next time.
Specifically ask her these exact questions and make these exact statements. She already wants you and she has already unconsciously made her decision. Trust me when I say that she is disappointed when you remind her of the thing she told you to say. She's flimsily trying to leave the responsibility of
both of your actions entirely on
you. By asking her these questions, you'll be clearing the smoke screen she has set up before her eyes and removing the safety net she's set up in case she wants to pull a blame game in the future. She just needs her conscious views changed a little to see things for what they are. She's deceiving herself into thinking that there is a big difference between oral sex and intercourse.
I can understand what you are going through though, this being your first time and all. Even though it seems quite daunting to convince your girlfriend to go ahead with it, this problem actually isn't a massive one. Ever notice how the shadow of something is much bigger than the object itself? What you are feeling is the shadow, but your issue is actually the little mouse in the corner.
Oh yeah, and her always saying that she is on her period is a blatant, transparent lie. Menstruation only lasts 3-5 days, so you could always track her times.

In fact, I tracked my girlfriend's period when we were still together so that I knew what her "danger days" were (the days she could get pregnant) so that I knew when it was okay to have unprotected sex and when it was best to wear a rubber or not have sex at all. So you might want to look into that if you're interested, or I could post another tut on the subject if you want.
That's pretty much it for the advice I can give. Ask her those questions I gave in the first paragraph, tell her those statements, open her eyes on the subject, and maybe track what she tells you with regard to her period, but I'm really emphasizing my first paragraph to help you.