Upvote:3
Yes, it's probably a good idea to renew your passport. The visa will be a full-page sticker that is affixed to your passport, and can't be moved to another passport. When your current passport expires, you would have to either:
You're going to want to have a new passport soon anyway, since you won't be able to do things like enter another country with an expired passport. It makes sense to renew your passport now and then apply for the visa.