What is the most appropriate time frame to apply to a Postdoc?
Charles answer here (https://academia.stackexchange.com/a/5303/4231) applies to your case. Some positions will start right away and some positions will have a fixed start date set in the future. I suggest you start looking around 6 months into your 1 year postdoc, at first focus on positions starting later: that info should be in the job advertisment. Then, if you have not found something suitable, focus on positions starting right away when you approach the end of your postdoc.

Do not wait until your postdoc is finished to look for a new position.