It is standard practice to discourage testing before 12 days past possible insemination, no matter the cycle length. Irregular cycles make it more difficult to determine when your body releases the egg, but if they performed an IUI, they probably got that pegged down. The worry with testing too early is what is called a "chemical pregnancy." In this case, the egg is successfully fertilized and begins the implantation process, but just doesn't finish "latching on to the uterine wall" before the body sends signals that it's time to menstrate. I don't know the specifics of your irregular cycle, but if you have a shorter leutal phase than that could be the problem you've had in conceiving.
You did not mention, but have you been on any hormone injections in preparation for the IUI? These can sometimes affect teest results, so keep that in mind.
In other news, even a very faint positive is positive! Although, the last time I took tests, I just didn't feel like I could trust the second line, so I bought one of the pregnancy tests that says "Pregnant." For some reason, seeing it in writing made me believe it more. Think good thoughts, visualize a strong, healthy baby, and treat your body like you're pregnant.
Good luck!