You know, it's up to you. She is lovely. Long in the back/loin, neck ties in high and appears from some of the photos to be short. Front legs look off, maybe camped out in the back. Personally I wouldn't after seeing the side shot, but it could just be the photo. No horse is perfect, she looks athletic and capable.
You said you want to keep the foal, train it as your own so there is no fault in that. You obvisouly know the costs associated with breeding and raising the foal so im sure you are prepared. She looks very loved and well cared for.
I agree it would be best to cross her so that the foal can be registered. What exactly is her performance record? I would think long and hard about the risks and time it's going take. She'll be out of commission for a while, will have a foal by her side for a year. It's tough. If you go the QH route maybe look into an equally athletic appendix bred QH/paint/pinto. Going with a foundation or reining/cutting horse could look wonky, I'd play up her athleticism.