If I were in your position, I'd go out and buy the gun now (renew the license later, when necessary).
Your concern seems to revolve around not wanting to purchase a gun when you have no guarantee that your license will be renewed in the near future. The exact opposite is true. If you own a gun of any description when your license comes up for renewal, the renewal is strengthened, not weakened.
There is no need to take any courses for the renewal. The renewal form will be mailed to your address of record with all the pertinent information already printed on it. You only need to:
- report any inaccuracies or changes to your info
- provide a recent photo (of a certain size, etc.)
- sign and date the renewal form
If you've had a major change such as marriage, separation, or divorce since your last license renewal, you may need to provide detail. If you're married or in a "conjugal" relationship, your spouse/partner may need to sign off, too.
There is no need and no advantage to applying for your renewal early. In fact, that would be a red flag, IMO. If you don't get your renewal form in the mail at least 2 months prior to expiry, then download the form and get it sent in ASAP, as you may have issues with your file at the CFC.
As has been correctly pointed out, there are no fees for simple license renewal.
ETA: Just remember that, once you own a gun, your renewal MUST occur prior to expiry of your existing license, or you have become a paper criminal (with possible repercussions to your eligibility to retain your guns and/or hold a license in the future).