I have a lot of animals running through my place all the time, and Penicillin is a pretty mild drug that helps with a common cold, and generally gets all the infection out of their bodies. J, I would make sure to call a vet and tell him the name of that penicillin because there is a couple types that are slightly different.
My vet recommends not to use one type because it isn't suited for horses. Anyways, make sure you have the correct type, then I would give your mare 1cc per 100lb of bodyweight. Usually with my yearlings, I do a 10cc injection for three days, and on the fourth morning, if they aren't better, take 'em to the vet! With your pony, I would give her 3-4cc's in the hindquarters. If you don't know what your doing in the neck, you can kill them.
Make sure you stick the needle at the top of the hindquarters, a couple inches behind the hip. Also, these shots don't bother some horses, but others get pretty mad and try to kick, so stand by their side, away from the hind legs.
If you ever have a big horse that needs more than 5cc's split the number and inject it in two different spots. Idk why, but that's what an old horse guy told me to do, and I've been doing it ever since. It probably absorbs faster, or maybe keeps them from getting sore.
Any new horse/animal that comes to my place gets a shot and gets wormed coming right off the trailer so I don't get cross - contamination. Its worked for me so far! Remember to call a vet about the penicillin because if it isn't the right kind, it will probably do more harm than good. Let us know how she does!