I have to "Estimate the order of accuracy (an integer power of h) by examining the behaviour of the error when h is divided by 10."
I have found the errors, how do I find the order of accuracy given these errors?
For h = 0.001, I got an error of 1.2325034326465811e-09.
Is this all I need to find the order of accuracy? If so, how do I use these to find it? If not, what else do I need to do?
You're asked to find the accuracy as an integer power of $h$, which means that your answer is going to be something like "The accuracy of the method is $O(h^3)$" (or $h^7$ or some other such expression).
If you're trying to do that numerically, then you could do that by calculating the error for several different values of $h$, and then trying to fit those to an equation of the form $\epsilon = kh^m$ (noting that the easiest way to do that is possibly to actually fit a linear relationship on $\log \epsilon = m \log h + K$.