If she has been playing a few years and is committed to the instrument, it may make sense to move up to a grenadilla wood model from the beginner ABS models. Wood instruments require more care, and can be damaged if dropped, but they have the ability to produce a wider variety of tones and will likely help her grow musically. Without speaking of a specific company or model... let's focus on the qualities you want: seasoned Grenadilla wood (meaning it rested for 10-15 years before being finished), forged solid metal keys (not plated), high quality cork, high quality pads, tight tolerances, tapered toneholes, and good ergonomics. The instrument needs to be efficient with air, and be easily able to transition across the registers (octaves), as well as allow for subtle changes in air and tone by the player. The clarinet itself is important, but the tone is affected very significantly by mouthpiece, ligature, and reed combo. Don't skimp on the mpc and lig.
Buying new clarinets makes little sense, as there are so many good used ones in the market, and clarinets lose 50% after being used about 2 years.
Used buying guidelines:
1. No cracks. If it has cracks, even repaired ones, just pass. Ideally, there are no chips either, but there may be tiny marks from use.
2. Try to find Solid nickel silver keys, which can be plated in sterling (look for discoloration from wear). You definitely don't want cheap "pot-metal" keys that are plated with a thin coat of shiny metal.
3. Wood that is oiled (look inside the bore and tenons) and has been maintained.
4. New cork and pads (this costs about $400-500 to perform on a used instrument). If you're buying used, you want a fully restored instrument
5. If you're not an expert, buy from a local music shop, or restorer. Ensure it has a full repad and cork replacement, and make sure you can return/exchange if unsatisfied.
6. If you wish to buy online and the instrument has not been fully restored, add $500 in assumed refurb costs.
Here are a few used professional models can be purchased for under $1,200 fully restored, or for $350-650 pre-restoration.
Selmer 9* , 10, 10G
Leblanc Noblet DN Model 45, Artist or Laureate (Pre 1980 is best)
Buffet Crampon R13
Yamaha YCL-650
The Buffet R13 is ubiquitous in highschool and college. They are very easy to find in great condition. If you want to go with Yamaha, skip the YCL 250 and get a used YCL 650. There are 5-6 of these on sale from Japan on ebay right now in the 400-800 range.
Best of luck,
David