There are 2 (possible) issues here.
You could be concerned about the age. This does raise a few concerns:
What happens if they break up?
Will she be able to cope? A number of people around my age have been in serious committed, sexual relationships and haven't worked out - for a number of reasons.
It often seems to be that those boys who will enter these relationships are likely to be the ones to be less committed and break it off. I may be making a generalisation here, but there could be a causal link between young sexual relationships, and the boy breaking it off (either cheating or moving on - perhaps getting bored).
This may not be a concern for you. I don't know what country you live in, or what the custom is. However, I know that in my country, there is a shocking distinction made: Even if both are underage, the male has committed statutory rape. Now this may not seem like a big thing - who is going to follow it up. But what if she starts to use that over him (not saying she will)? She could claim rape, which is not a good place for a 14 year old boy to be in - a sex offender at that age does limit job prospects.
However, this may not be an issue for you - you may feel it is acceptable or the law may be fine with this.
Pregnancy, protection and STIs
Pregnancy is not a lighthearted matter. Whether you agree with Abortion or not, it's a painful process (emotionally) and giving birth at 15 is really quite dangerous in some cases. Not only that, having a child is a big, big responsibility as you know, and still being at school when that happens is likely to limit her attention to education.
Maybe this isn't an issue, and you would be happy with abortion? Next issue, protection.
Protection links in between STIs and pregnancy. Condoms are typically the best preventative measure for both of these. The pill is a nice backup, but I wouldn't want to be going through treatment at that age.
You can get them both tested together, but they're 14 years old. I don't wish to judge, but are they trustworthy, are they going to stay together, and is either likely to cheat? As mentioned above, at that age, it can be hard, and it is often the boy who will get bored and (maybe) move on.
STIs are also no joke. Depending on where you live the treatment can be expensive and hard to access, and it's not something anyone needs. Interrupting education for hospital appointments is likely to be detrimental and also embarrassing if anyone finds out why.
Revenge. This is unlikely, but if they break up, how would they react? If they are close enough to be sleeping together, one would hope they are close enough to have shared personal details with each other. Revenge is a real thing that does happen - is she sending explicit photographs that he could post online? Is he someone who would go around school saying she is easy? With the online world at everyone's fingertips, your reputation is important. Her mental state would not be great after a breakup with revenge.
This is normal in a lot of cultures. There is a little concern about "inbred" genetic disorders, but as mentioned in other answers, there is genetic screening (although this links back to Abortion, so you may disagree).
Two relationships. They are going to have 2 different relationships in a way. Aside from the (probably inevitable) breakup issues, they are going to know each other in one way, and then in a separate way. How will they behave around family? As a couple or as cousins? Going back to a breakup - my family is big on "BFGs", or "Big Family Get-Togethers". How would being forced together with your ex be? How would it be if your family are expecting you to be happy to see each other?
I wouldn't want to be in that situation.
It's a difficult one this. You should still be the one deciding - you're her legal guardian and at 14 years old, it's likely you know best. However, I doubt you're going to be able to make the decision for them. My opinion - 14 years is too young to be making life changing (?) decisions. Especially with the added risk with their chosen activity. I'd also be concerned about the breakup. I'm sure they will think they will be together forever, and probably get married, but that doesn't mean they will.
I know my son wants to be with his girlfriend forever - and I believe they can (and probably will). But that doesn't mean there is no chance of a messy breakup, especially because of their current situation - BFGs are not going to help this.
My apologies if I've been stereotypical / offered my opinion too much. My observations are mainly formed from what I've seen at school, with people in young sexual relationships that don't work - and I don't want yet more people go through the process I've watched so many others go through (especially as I've supported a number of them).