Morning Jim,
I would agree with Rutty that possibly the FAS604 or the replacement FAS6004 might be suitable, as it is relatively light albeit needing some effort to cock it. These could be at the relatively economical end of the price scale if you can find one.
As an alternative pistol that can be grown into, the Hammerli AP20 might be worth looking at. This pistol has a relatively small grip, looks modern and will outshoot your daughter for many years. This is a PCP air pistol which would need the cylinders refilling from a dive cylinder. Unfortunately being a newer style of pistol, the price tends to go up, even if you find a second hand one.
You might be able to get some ideas from the other shooters at the pony club or even from the people running the shooting range.
Hope that this might be of some help to you.
Regards John