Yes, it would be helpful if you can clarify what exactly she's doing in the private lessons, a jump off is usually the tie-breaker at the end of a showjumping competition where riders compete to jump the quickest clear round, so an odd thing to be doing in a private lesson with no-one to compete against! Does she always ride the same pony or is she getting experience with a variety of different ones?
In general terms of progression, I wouldn't be expecting her to jump every lesson even if that's what she likes best, nor is it a race to see how high she can jump, although kids often think it is! The things NameChanger mentions (different kinds of jump, gridwork, short courses) are great ways to improve her jumping. She should also be working on her flatwork and starting to understand how to school the horse and improve its way of going, as well as improve her own position and effectiveness as a rider (both of which will improve her jumping as well!). She could look at the different British Dressage test levels, work out what level she's riding at at the moment for flatwork and ask if she can start to learn some of the exercises from the next level up - ideas to mention to her instructor could be e.g. medium trots, simple changes of canter leads through trot, walk-canter-walk transitions, basic lateral work like leg yields and shoulder ins, all should be achievable by a capable 11 year old on a well schooled pony (whether your riding school has such a pony is another question!) . As she improves she should also have the chance to do some different fun things such as XC, hacking, mounted games etc, not just ride in the arena all the time.
As to how to achieve this, I think more saddle time could well be a good thing for her - she may also start to find the private lessons a little dull. Loaning or buying a pony is of course a way to achieve this but a major commitment that can end up affecting the whole family so really not to be entered into lightly especially as you are not horsey yourself. An 11 year old is not able to take responsibility for the full-time care of an animal so you'd need to pay for full livery or do it yourself. Please don't feel obliged to do this, very many pony mad little girls don't get their own ponies until they are adults but can still have fun and learn!
Some ideas which are a bit less of a commitment: if you can find one, a good group lesson with others of a similar age and ability can be great fun for kids, they usually get an hour for the same price as a private half hour. Does her PC do camp, badges etc, they are a good way to motivate and progress (if not can you ask the leader if they can start?). Some riding schools do a 'share' scheme where the kids can come and ride +look after one of the school ponies a few times a week for a fee (a bit like a lease), which can feel more like having your own without as much commitment! Or finally in a few years she will be old enough to help out at a riding school at a weekend, good way to get horse care experience and often the kids are 'paid' with free or discount riding lessons...