I presume the vet has deemed her pregnant - right?
If so, lets look at some possible problems. If both sire and dam carry dwarfism, certainly a dwarf foal might be possible. Since there is not test for it yet, you will just have to hope for the best. However, this possibility exists in any breeding of Minis.
She is young but many are bred at that age and carry successfully. Since you say the sire is smaller than her, I'd say she should be ok. Know though, that all Minis, whatever their age, are prone to foaling problems, so I hope you are prepared for this eventuality. Belonging to the Li'l Beginnings Miniature forum, would help you a long way to getting a ton of help from those who go through it all the time.
Please don't listen to, or believe, all the myths put about re. Inbred offspring being wierd, having 5 legs etc. It is just not true. Just know that many responsible and knowledgeable breeders, inbreed just to set type. The foal will no doubt, look much like the sire's side of the family. This breeding has doubled up though, on all good points and probably bad faults, which might be in the sire's line. Hopefully, since he has been kept as a stud, he is of top quality and has near perfect conformation.
The problem as I see it, is that starting now, you need to really
work with this mare. By the time she foals, she should be allowing you and others, to touch every part of her body. You won't need her feaking out and trying to get away from you, if she does run into difficulties foaling. What are her favourite treats? Have quiet men offer them to her. She'll soon come around and get the idea that men are not all bad.
Make sure she has all her shots necessary. Make sure you have a stall ready for her when she foals and have her used to it before the foaling date. Don't allow her to be foaling somewhere out in a field with no light, in case of problems. A camera setup would be good, so she can be watched from the house. I'd keep her stalled in the night, a month before you think her due date might be. Monitor her feed intake too.
Have your foaling equipment ready and within reach, a month before you think she will foal. Don't allow many people except those she knows and already trusts, to be watching quietly, when she starts labour. Only assist if she needs it. Dimly lighted is best. Just enough so you can see what you and she are doing. She will most probably foal at night. If you see signs that she is close, then take turns with someone to watch her.
Oh - and I hope you have fixed all the fencing, so you don't have all this worry again in the future.