At her age, I would do the root canal. However, there are some complications which can affect the long term prognosis of the root canal. Since she is 15, the tip of the root would have just finished forming and the fact that the tooth was completely evulsed, might cause the root canal to fail at some point in the future. The root canal is the best option at this point and it keeps the bone in place in the event the root canal fails, tooth would need to be extracted, and a retainer with a false tooth (also known as a flipper) placed as the extraction site heals, preparing her for an implant later.
LCOL here, ballpark for upper root canal less than $1000 with a filling to close it, not a crown/cap at her age VS Extraction $300. flipper retainer w a replacement tooth $150. Implant surgery $2500, implant crown $1500, not counting possibility of bone grafts.
If if you do go with the implant, make sure you take her to a periodontist that does implants. They will be better with esthetics like needing to contour the gum, than an oral surgeon.
Good luck!