Strangely
You sound precisely like me a year ago at 34. I'd returned to running a year or two before after being out of it since my teens, but it was purely on a casual once-a-week basis. Having just gone sub-40 for 10K, I ramped up the mileage fairly sharply over a period of a few months, in the fear that I was running out of time to see how much I could improve.
Whilst it would fit nicely with the advice you've received so far to say that it resulted in me breaking down and getting injured, it wouldn't be true. I got away with it (so far), and have lowered my 10K PB to low 34. However, unlike you, I wouldn't attribute it to being less injury-prone than other people - rather, it was pure, raw luck on my part.
The advice on here is the right advice. You can, of course, like I did, take a risk with your body, and you may be lucky and get away scott free, but more likely is that injury will strike and you will take longer to hit your goals, or not hit them at all. It is your body and your choice at the end of the day, but I would say that the motivation of feeling like you are running out of time is, in hindsight, a load of baloney. There is plenty of improvement to be made in both your 30s and 40s, and the limiting factor preventing you hitting your full potential is far more likely to be your training schedule and how that fits into your life than age. Quite apart from anything else, building up slowly could well see you making decent improvements for some time yet, which could be more rewarding than a quick improvement followed by a relative plateau.
Edited: 19/09/2012 at 13:20