I haven't really thought about this before, but Ok here goes for a serious answer: I'll try my best for 2 am
First a question: is it your first cousin? If you think it doesn't matter: a cousin is family and this is wrong, and it doesn't matter how distantly related they are, consider this:
1: any two caucasian people will be 50th cousins at the most. I read this from more then one place but I cbf finding sources, look it up yourself.
Even if this is not completely accurate, the figure will be close to this probably. It makes sense, we all have to be related eventually, I mean think about how the population of the world has risen so rapidly in the last few thousand years.
So if all people are cousins, (pretty much) then where do you draw the line between acceptable and unacceptable? 5th Cousin? 4th? 3rd?
To think about how you might answer this question, I guess you might want to consider why we see relationships with cousins wrong
I feel this way too, everyone does, It just feels wrong and icky, but surely morality should be more then just our biological gut reaction. I find gay sex yuck and icky to think about, but I believe that gay people have the right to do what they want in the privacy of their own homes, and that they have the right to be in gay relationships.
Logically the only reason to draw a line I can think of in the case of cousin couples is when cousins knowingly bring a child into a world that will have a disadvantage and genetic disorder. And even then, this isn't an argument against a relationship, just an argument against having children with a cousin. On top of that I've heard cousin couples argue on a documentary or something like that once that this chance of genetic illness is the same for first cousins as it is for older couples, say over 40, and that third and fourth cousins actually have healthier children then the average, but I haven't checked any of these claims because I haven't really thought about this issue much before. And even if there was a more significant chance of their children having genetic disorders, many people would still say they should have a right to take that risk.
Also apparantly cousin couples are very common in some cultures. I think this is trivial and don't really see this as an "argument" for anything at all, it might comfort you a bit though.
Another trivial fun fact that might cheer you up but doesn't prove anything about what is right in this situation: We're all the product of cousin couples. Think about this, each generation you go back, you double the number of ancestors, but there were less people as time goes back further. Look here for more information http://www.straightdope.com/columns...ys-have-more-ancestors-as-you-go-back-in-time
So it looks like there's nothing wrong with having a relationship with your cousin, and that no line should be drawn at all, BUT
1. your cousin may not feel the same way, yet
2. your family may not feel the same way, yet
3. society at large finds it a little icky still
If no one knows that they are your cousin this might avoid the 3rd one to some extent but... There will be issues if you decide to go through with this. Probably, unless your family are all highly intelligent tolerant awesome people. Which is unlikely, this is Australia after all.
I hope I've helped.