12.3hh is not neccessarily a B and is certainly not an A. As stand up to 12hh, Bs and Cs both from 12hh to 13.2hh. A B won't carry as much weight comfortably as a C generally; but that said, I know a farmer weighing 11 stone and getting on for 6' tall who had a 13hh B that he regularly rode on the farm before he got a quad bike. Said pony coped more than happily with that and worked well into his twenties.
But there's a huge difference between a well-built, fit, working B with plenty of bone and girth, and the lighter ponies that don't have the same substance. There are also plenty of lighter-boned Cs around that wouldn't be up to an adult's weight.
There are several things to bear in mind. First is that you are quite tall; so that can make some ponies not used to taller riders feel very unbalanced. The pony is not fit; so any ridden work will be hard - carrying an adult even more so. The saddle needs to fit both of you; that is not always easy to do, especially as it needs to spread your weight over a wide area at the same time as not interfering with the pony's loins or shoulders. Finally, you'd need to look at the pony's build, and way of going. A pony that already moves well and has a good strong topline will cope better than one whose topline is less well developed or who is lighter in build. Conformation like sickle hocks, weak loins, and so on will also have an impact on what they can carry.
If you like the pony but worry about being too big, would it maybe be feasible to teach her to drive instead?