I agree ^ lastqueen . And sorry to immediately go to the distasteful subject of money, but even if you are lucky enough to have the substantially into 5 figures budget to buy a 'school-master' it's going to be quite a high power ride and not necessarily a point and go confidence builder so she needs to be sure she will enjoy riding that kind of horse. I don't mean a beginners bombproof plod kind of schoolmaster (she's clearly past needing that), but more the competitive amateur's schoolmaster who will take her around her first BE Novice or BS Foxhunter, i.e. the horse who is not only talented enough to jump the height with ease, but also kind/brave enough to still go if not presented perfectly at every fence and hand-held around the whole course pro-rider style - that type of horse is not necessarily a saint or 'easy ride' in most people's books! The dressage schoolmaster at our yard who is schooled up to Intermediate and described as 'push-button' by his owner will dump you in a heartbeat if the buttons you push are the wrong ones! I have been that dumpee and it wasn't much fun

And actually unless you have £15k+ going spare, and particularly if you were thinking to loan her current boy out rather than sell (so you won't have the money from the sale to put towards next horse), you may need to look at buying something which isn't a perfect schoolmaster and which has 'quirks', i.e. perhaps not great to hack, not great on the ground, or particularly hot/strong (or broken down/unsound, but I wouldn't advise that!) - that might be absolutely fine for her and just a case of finding the right match of course (e.g. some people are fine with nappy but hate hot/strong, others are vice versa!). But if her current boy is lovely and easy in every way she may find she misses just being able to hack around with her friends or pop out to a fun ride or whatever without drama.
Or of course the other way to get a high powered competition horse for less money is to buy a youngster bred for the job and bring them through the ranks yourself, which could be a great long-term project for her if she's prepared to be patient and put in the work. She would need a lot of help from instructors etc to bring on her first ever youngster but I assume she'd be having lessons regularly in any case?
But overall I'd be a bit concerned whether a time in her life when she might have a lot else going on with applying for college, first job etc., is now the time to take on such a big commitment? And I know from my own experience with teenagers that sometimes the bigger the commitment/investment the more anxious and/or ambivalent they can get about it so I would wonder how she'd feel about knowing you've spent such an enormous amount of money into buying her a competition horse, would that spur her on or put her off more do you think?
Ultimately she's an incredibly lucky girl to have a horse of her own at her age at all, and her current boy sounds lovely. If he is able to comfortably jump 1.10m ish (is that a single fence or course, SJ or XC?), it's not as though she can't compete at all or is limited to kiddy classes or clear rounds, it sounds as though she could aim to do a BE100 or BS Disco grassroots championship series, which is a pretty good level for an amateur on their first horse (many wouldn't ever go higher!). She could look into doing local leagues and pro rider clinics so she's more honing her competitiveness at that level, doing more technical fences, being more effective as a rider etc., rather than just progressing up the height levels per se. And she could then work towards earning enough money herself to afford her next horse in a few years (perhaps still with a little help from Mum!)...?