I suspect the first question to ask yourself, is why you want to breed. If it's to get something like her, chances are you won't, because the baby will be half of some other horse and might not look or act like she does.
If the baby is to be for sale, then know you will be competing with thousands of others also trying to sell their foals.
If you plan to keep the baby, make sure you know you can reasonably afford another mouth to feed and have the time to train a youngster. Also remember our lives change and at some point you might have to put the baby or youngster for sale, even if you'd planned to keep it.
What about your mare? She could live another 10 or even 20 years, so if it's a replacement your are after, she could quite well outlive her offspring.
While she's not elderly, she's not young either. Are you willing to put her life in jeapardy just to get a foal, when there are thousands of lovely horses being shipped off to slaughter every day now?
We take a risk when breeding any of our mares.
If you are willing to take the risk, then you'll need to evaluate her very carefully. What are her strong and weak points? What can she offer the breed?
What does her pedigree look like? Will you be linebreeding to a horse you like or outcrossing?
Are you very well aquainted with the horses in her pedigree. You should be if you wish to become a breeder. And if you breed just one foal in your life, it does make you a breeder.
You'll need to do tons of homework to pick a stud horse who is excellent where she is faulty. Would you be willing to send her to be bred or purchase frozen semen? Are you aware of stud fees and/or AI costs to the vet? You might also have a problem getting or keeping her in foal and the costs add up.
Breeding to the nearest Arab stallion down the road, won't be good enough and besides he's probably already got many offspring locally, up for sale.
Since your mare hasn't been bred before, you'll need to have a look at the offspring your chosen stud has sired and from mares hopefully much like yours or with a pedigree close to your mare's.
Lots to think about. If I only had one horse now and an older mare at that, I'd probably not breed but purchase one of the thousands of good horses out there for sale at very reasonable prices.
Certainly many older mares are bred. I know of one mare who has had over 20 offspring. She's old now and no longer gets in foal at all.
On the other hand, an old Saddlebred friend of mine, bred her mare for the first time when she was also 21 and everything went well. But the older they are and especially as a maiden, the more problems which might arise.
I'm not telling to breed or not to breed. The decision will be up to you as her owner. There's just lots to consider.