the biggest thing you can do for your daughter to ensure her success is to instill confidence in her. If she is confident in her shooting ability then she'll be able to be successful when it comes time to take the shot. Confidence will do more to ensure success than any advantage one cartridge will give over another.
+1.
While not the fan of the .223 for deer that taylorce1 is, I can not agree with the above statement more.
My eldest daughter uses a .30/30 ....... in open country, and with a great deal of success- because she knows the gun and believes in her ability to use it with the same conviction she knows she can swim, or drive, or any other skill she has practiced.
Practice is Priceless, and Practical Practice even moreso: Establish that the gun and load and sights/scope work, and then move off the bench, and shoot as much from field positions as possible.......
Finding a gun that fits your daughter is more important than what caliber it is chambered in ......