My personal opinion is that there is probably no safer time to fly, as I am sure that the date is a stark reminder to security services that they need to be ultra-vigilant.
We fly on the 12th and I haven't given any consideration to allowing the date to affect our plans.
We flew in 2002 on the 13th Sept and had no problems.
I was in New York in April with my WTB and we took the time to pay our respects at the former site of the WTC. It was a very moving atmosphere and so it is clear that people will not forget. With this in mind, I am certain that those who wish to will take 5 minutes out of their day to offer their thoughts, however, moments of silence are probably best kept in the areas affected (NYC, Washington DC & Pennsylvania).
Just my opinion, UK citizen with no direct link to what happened that day. I haven't forgotten and feel I have paid a suitable amount of respect to the unfortunate ones, however, as a nation victimised by terrorism (IRA) for 30 years or more, we do not hold moments silences for each attack, but also never forget.