I'd recommend either the Savage Axis or Ruger American. These recent introductions are value-priced, but modern quality pieces of good o'all design. (function, ergonomics) Both offer compact/youth models in .243, including camo & lady-like color options for the Axis. Both also have detachable magazines (meh) and user-adjustable triggers (yes!). I'd gladly hunt with either of these and not feel under-gunned with the caliber or o'all length. (Ruger's 'youth' has 18" barrel & Sav's has 20" if that matters)
Your little lady may feel she's outgrown the caliber someday, but not necessarily the rifle. As long-armed as I am I find it so true that a tall person can handle (aim) a compact much better than one of small stature can handle a full-size rifle (14" LOP, etc). That said, there's much to be said about using a slip-over pad later on to bring the sights/scope up to the eye without tilting the head so far. If she becomes attached to the particular gun that option will always be there.
Two of my .243s are NEFs and I like 'em, but if your young hunter will likely be shooting bolt actions as she gets older (Rem, Browning, etc) it's never to soon to get her acquainted with working/clearing the action, and working the safety. Fit to the shooter is very important so I'd advise that you have her try out each possible candidate, whichever you consider.