I’m not a PT or an OT but I am vastly experienced in broken bones in childhood. Especially early childhood. Myself and both my children have Osteogenesis Imperfecta (brittle bone disorder) and have dozens of fractures between us.
Though as a child we broke our legs (mostly femurs) and endured spinal compression fractures the most, muscle weakness was absolutely a side effect of being in casts for extended periods.
Does your child tolerate pressure on the casted arm yet? It’s not unusual for them to walk, crawl, on the casted and broken limb. Don’t discourage it, the cast keeps the bones safe. In fact to keep muscle strength up I would even encourage some crawling on that arm if she tolerates pressure and weight of her own accord. Don’t ask her to do this, only do it if she is doing it already on her own. The day my daughter walked in a body cast floored me (she was 23 months old), but it really helped retain some muscle strength.
Casts are heavy, even fibre glass ones, so the simple weight of the cast and just having her gently (when tolerable, you don’t want her in pain) is a lot of good muscle working out.
The chances are likely that there will be strength discrepancies regardless of exercises once the cast is removed. We noticed it returns to normal within 6 weeks though. Seek PT and OT after the cast is removed and they should help guide you on ensuring a return to where she was at.
Good luck! Honestly if you need any other broken bone or casts questions feel free to ask them Hope she mends well and fast.