Youngsters, young or old, can benefit from appropriate strengthening exercise. What's appropriate depends on their age. The American Academy of Pediatrics does not recommend that children under age 10 use free weights or exercise machines. Studies have found children under age 10 are more prone to injury than adults are - they might drop or trip over the weights; they tend to become impatient and do the moves too quickly. But boys and girls, under age 10, can do strengthening exercises that use body weight: sit-ups, push-ups, pull-ups, stationary jumps, and hill runs.
New evidence suggests that children older than 10 can safely strength train with equipment, and will gain important benefits: increased muscle strength and muscle mass, plus improved general fitness.
The National Strength and Conditioning Association recently published these safety guidelines for older children who do strength training:
If your daughter wants to train with you - and you are confident that she is mature enough to follow your instructions - this can be a great activity for both of you.
Be sure to teach her all the safety guidelines such as breathing properly, stowing the weights, lifting smoothly and slowly, etc. I suggest you focus on the exercises that use body weight and dumbbells, since adult-size ankle weights probably won't fit her properly. Start with very light weight and progress slowly.
I hope you both enjoy these mother-daughter workouts!