You are mistaken about the palindromic date....11th november 1111 for a start. and 01/01 1010.
In 1001 the Christian world was going through the same millennial panic that it went through in a milder form 1,000 years later. Tourists flocked to Jerusalem to await the second coming for the next century, causing the governor to close the roads, and kicking off the crusades.
As to what will happen ... you will magically become one year older. Its just a number. I remember thinking there was something magical about 12.34 on the 5 June '78 (think about it) but it turned out that we still had a maths test that afternoon.