Congratulations on the new horse!
I thoroughly agree with the previous posters, I just have a smidge more to say. :)
I would recommend that you consider getting this book: Amazon
.com: Equine Fitness: A Program of..."> Amazon.com: Equine Fitness: A Program of...
It's fantastic at outlining what and how much to do to build muscle on your horse. It even has a special "older horses" section that outlines exercises that specifically target problem areas in senior horses.
Also, side note, according to that book (which references studies and stuff), it can take a year or more for the internal structures of a horse to become strong after becoming weak. So, even once she looks and seems 100%, her ligaments and tendons are still going to be playing catch up. It's just something to keep in mind. It doesn't sound to me like you're going too fast but be careful. :)
Do you have access to hills? Hills are fantastic for gaining muscle, especially topline muscle.
ETA: I'm thinking 10-15 minutes max. Of trotting. Since she is so undermuscled, the strain and torque of circles at high speed (lunging/roundpenning) is going to be so much worse for her than it would be if she were going in a straight line. In a straight line 15-20 minutes would probably be ok but I wouldn't do that to her on the lune line/in the round pen.
Do you have access to an arena where you could free lunge her? That's something I forgot to mention. I'm of the opinion that free lunging is fantastic for horses, especially those who are under muscled. I found with my mare that she learned how to carry herself (since the lunge line pulls on the horse, no matter how loose it is) so much better due to being free lunged and there's less torque and strain on her legs because she'll be moving in more of a large rectangle vs a circle. And! Side benefit: she'll learn to watch your body language more closely for cues because you're farther from her.