If you are an AQHA member you will have "free money" every month you can do pedigree research with, its in their members section once you log in. If you are not a current member you will be unable to look up horses this way, and will need to ask someone who is, or hope your mares ancestors are in All Breed Pedigree Query
already, which you may be able to set up yourself if you have her papers to look at.
The questions you need to ask yourself are:
Is my mare an excellent example of her breed conformationally?
Is she an excellent example of her breeds temperament?
What has she done in her life that qualifies her as breeding quality? (ie. show record, offspring record, great bloodlines AS WELL AS
great conformation and temperament, or is/was she a great using ranch horse?
What are you breeding for exactly? Do you have a goal in mind for the foal and what is it? Where does she fit in to that goal and can you name the qualities she has that you would want in your potential prospect whom you wish to use for that particular goal?
What are your plans with the foal should it turn out to be the opposite of what you are looking for? In other words, is there a market for the foal should you not want to keep it or should you need to sell it? Would you send it to auction where it would potentially sell to meat buyers? You won't be able to ride it for at least 2 years... are you financially capable of keeping, caring for, and training a young foal until its time for saddle training?
What exactly is your experience with horses? Have you raised foals before? Have you trained horses yourself before? If not who will be helping you properly halter break and desensitize this baby to every day activities (ie. teaching ground manners such as leading, tying, picking up feet, vetting, farrier care, etc) so baby is safe to handle?
If your goal is only to have a cute wittle baby you can raise, you are breeding for the wrong reason. If that is the case, there are TONS of perfectly healthy weanlings/yearlings and younger horses as well as older already broke horses that are going through auctions for cheap, I'm sure you can find something that fits your goal(s) in there and potentially save them from making a trip to slaughter.
What is your mares breeding? If you offer up pics (standing square, both sides, front, and rear) I'm sure people on here will be more than willing to give advice on if you should or shouldn't breed, and if so, what type of stallion would compliment her.