I think you're underestimating your own shelf life there. I know from personal experience that most people in their 60s are capable drivers (provided they were capable drivers to start with -- age doesn't imply competence). What they have lost in reaction time and processing ability (which is not as much as previous generations at the same age), they are able to compensate with experience. Just by handling less information through better front-end filters, they solve the problem just fine. At some point the two curves will cross, at which point it does become time to hand over the keys, but for healthy people this is probably going to be north of 70, and possibly even north of 80. By then, you might not even need to do the driving.
Even in my grandmother's generation (I'm about the same age you are), she didn't actually become a rolling hazard until she was pushing 80, and that was largely because she made navigation errors and then did stupid things to attempt to correct for them. The basic mechanics of driving and not hitting things still operated passably, although she really had no business being on the road. Fortunately, her circle of travel shrunk with her abilities.