So, to be clear, I think I've done DD a slight injustice. That is, she showed me the design (which she claims she made herself) as something she'd like tattooed but didn't make a request to have it done - I figured she was heavily hinting and said 'so are you wanting it for your birthday' to which she excitedly said 'Can I?' I told her I'd think about it.
She definitely would never just go off and get it done - she really is such a good girl. Also, we're friends with a very good tattoo artist who does home work - which, again, she is aware of. I think she presumes that if I were to say yes, that we would get him over to do it (we would). DP has an awful red devil (yes, he supports manchester united) that he had done when he was 16 - he regrets it although he puts it into perspective of 'growing up' and at least he had the brains to get it 'out of sight'. He has gone on to have three others that he doesn't regret at all - I think his experience will be useful in speaking to her which ever way I decide.
I am still torn. I think, I know I've been quite slack as an attentive parent this past year or so - I've found it difficult to impossible to go to her target setting/performances yet she is still slogging away hard (she's already taken her gcse in english and got a B). And she really never asks for anything (and, technically hasn't asked for this - although I know her so well and I know she was hinting!). My hang ups about rules are something that annoy me - I mean, yes, the law says 18 but... why do I unquestioningly accept that? Don't kill people, rob them, rape them, yup, I'm all on board with those rules, but those that affect nobody other than the person making the decision? I do question those. These things are subjective - and do not take into account that some 18 yer olds still do not have the capacity to make important decisions.
Of course, I would ensure it's discreet in both size and location.
I don't know! I think I am erring on the side of allowing it - to assuage my own guiilt? Not sure? To rebel against my own fixation on rules? Not sure? Because she deserves it? I think she does - although I know she would completely accept it if I told her she has to wait until she's 18.
Argh! This parenting lark never really gets easier! 
Plese keep opinions coming. It really is helping me process. And... wil save me posting in AIBU for the first time (which I will no doubt regret when everyone jumps on me!)
By the way pixie was DD's friend the same age as her? Because if so, who the heck was she getting vajazzled for?! Who was gonna be enjoying it?! I don't buy decoration of her pubis is for herself! 