i wouldn't recommend it. you're at about adult size and you describe her as a late bloomer, presumably in other areas of her development as well - and she's thirteen. it sounds like you could hurt her if she did allow you to have sex with her.
[that said, around 14 for a first period isn't that late, honestly]
do you know her current boundaries? you need to start from there. doing too much will probably freak her out a little bit. warming up to that idea naturally takes time, especially since women tend not to be as sexually driven as men - not always, of course. if you know your current boundaries, work slowly from there - like, if she'll let you make out with her, feel her up a bit or something [probably around the upper half, since lower would probably feel more invasive to her]. i won't give a step-by-step analysis for it, as it's largely personal, but just use your head. you don't seem like an idiot. time also helps, too. if she's known you for a long time and trusts you, she's likely to be more willing to open up to you - in more ways than one.
but, please, for the love of god, don't be one of those people who expect sex from someone and if they don't get it bitch about how nice guys finish last. in the end it should be that you actually care about them - not just because you want a good fuck - in a romantic relationship. while "friends with benefits" and such do exist, if that's what you want it should be admitted up-front. don't sneak around or whatever. there are other people who want nothing aside from sex from a person, and that's fine, but let it be known. no need to lead anyone on or break any hearts if she's expecting something you're not gonna give her.
edit i omitted this part because it seemed obvious to me but maybe it's because i've been in my mother's custody since i was eight, and have thus had to deal with a lot of female!problems.
i really hope that you understand something; she's likely a virgin, right? giving it away is something that a lot of girls take very seriously and it means a lot to them - and if she'd consider it with you, it's not exactly a trifling matter. that's probably another reason why they're more cautious and conservative about the people they screw; it's more important to them [and they are stuck with the baby if you fuck up/don't abort]. for a lot of chicks it's about the emotional aspect of sex, rather than the physical, and they really need to trust you in order to really enjoy it. pressuring them will not help, which is what i've been trying to say. you can't just get your virginity back, and if you pressure her into it, she'll resent you for it and probably feel like shit. wait, though, and with her trust and love comes her willingness [and possibly eagerness] to please you. it's not like women are [necessarily] selfish bitches, it's just that they operate differently and have different needs.
so, yeah, consider everything.