Weakness in a 10 month old kitten is not normal. Did your vet give you any ideas as to why she is weak? Getting her stronger doesn't necessarily mean building muscle. She may just need a good diet, to stay hydrated and get enough rest. Have you had her tested for worms? Make sure she is treated for fleas, as they can cause kittens to become anaemic, sometimes causing weakness.
Something else you can do is feed her as much kitten glop as she wants.
Home-made kitten formula (Kitten Glop)
8 ounces water (boiled then cooled)
1 envelope Knox unflavored gelatin
8 ounces whole evaporated milk (not skim)
1 tablespoons mayonnaise (not low fat)
2 tablespoons plain yogurt (not low fat)
1 large or 2 small eggs yolks (raw)
1 teaspoon clear Karo syrup
* 1-3 drops liquid pet vitamins
* 1 capsule acidophilus
* 1 drop Grapefruit Seed Extract (GSE)
* Optional, though very beneficial.
Boil the water, add the gelatin and mix well. Add the following ingredients in order, mixing well after each addition:
1/2 of the canned milk
Mayonnaise and Yogurt
Rest of the milk
All other ingredients
You can substitute canned goat's milk for the canned evaporated milk, if you prefer it. This mixture will keep in the fridge for up to four days. It is jello-like in consistency in the fridge so you can just scoop out as much as you need and warm. It can also be frozen in ice cube trays and defrosted as needed. You can find pet vitamins at a pet store or your vet, and acidophilus and GSE in the liquid form at a good health food store.