My trainer's foundation broodmare carried her last foal successfully at, I believe 21 or 22. This was obviously a very experienced mare (had a total of 16 foals).
If Fannie hasn't had any foals yet, you wouldn't want to wait so long. Maiden mares often have more trouble as they get older. A friend considered breeding her FEI dressage mare at 16, and after talking to several vets, decided against it. She didn't feel it was worth the risk to the mare's life. I would talk to your vet to get a more accurate idea based on your particular mare. Personally, I think between 10 - 12 is probably about the oldest maiden birth I would risk.
Please keep in mind, everything that is involved in deciding whether to breed a dog goes for horses as well. Is Fannie a good representative of her breed or sport-type? Have you carefully evaluated her conformation to determine the good and bad points? Has an un-biased professional done the same? What do you hope to improve in her foal? Has your vet examined her for signs of any genetic abnomalities/illnesses? What are your goals for that foal? Picking the stallion is incredibly important. You need one who will balance out the weaker points in your mare. In turn, your mare should balance his. No horse is perfect, and beware the stallion owner who claims his is
Be sure his temperment is one that you will be happy having in your foal. DO NOT SKIMP on the stud fee - it is one of the cheapest parts of breeding your horse. Put the extra money into getting the right stallion, not just your neighbor's down the road because it is cheap or a pretty color.
Remember, breeding horses is very expensive and an absolute crapshoot. I'll be honest, if you know Fannie's bloodlines, I'd be more inclined to look for a similarly bred horse who is a couple of years old. It gives you the ability to really pick and choose the traits you desire.
Keep us informed! Having spent so much time on a breeding farm, I do love stallion shopping!