It's never too early, but you have to start with your current abilities and ramp up from there. Find a good plan and you can stretch it out as needed. One good source is HalHigdon.com. The summer gets pretty warm and can slow you down so taking the extra time can be a good thing.
I agree it is never to early to start training.
Right now you want to be laying the foundation that your will be building on to run the half.
Personally I would not want to start the training program for the half if I could not easily go out and run 7 miles.
you need to find yourself a good half marathon training program on the internet and make sure that you could easily handle the first few weeks of it.
Getting Fit at Fifty
Can we assume that you are starting from not being a runner and intend to run a half marathon in not quite 8 months?
There are different aspects to training, and where you start from matters a great deal. If you are starting as a non-runner, then there's an entire level of training required just to get your body ready for the challenge of running 13.1 miles. That training is different from the training that you do leading up to doing the race itself.
Training targeted for a specific race can begin too early. Training to be able to run the distance - that you cannot begin too early - but you can begin too late.
I think Peter says it best. You really wouldn't want a race specific program 8 months out, but training overall can never be too early. You need to build a base, and the sooner you do that the better.