Perhaps let your little sister read this thread, maybe it will help her to learn more about the reasons behind breeding.
Cmaire, what they are talking about is that the registered half breeds (I'll only discuss the AQHA and Appendix horses as I don't know much about the Arab registry) is that both parents are still registered and you can still track their lineage. You know what their lines are and you can look back at their parents and grandparents to see what kind of conformation runs in those lines. Knowing the lineage is also useful for tracking genetic diseases. For example, many people won't buy a horse with Impressive on the papers even if the horse is N/N just because of the stigma attached to that name. People buy grade horses every single day and many of the N/H progeny in recent years have been left unregistered because they are N/H. That means when a person decides to breed their grade mare because she's cute or because she's sweet, they could be creating another horse with a completely avoidable affliction.
Now, I'm just using this as an example but if the OP's mare happened to be Impressive bred and was a non-symptomatic N/H, then there is a chance that the foal could be born N/H too. Both of them could theoretically live long and productive lives and remain asymptomatic....or they could both start showing symptoms and be dead in a month.
In the case of the OP's mare, they only know that she is a QH cross. Since they don't know what the other half of her lineage is (and likely her QH parent wasn't registered either so that lineage is completely unknown), there is a huge risk for some freaky conformational or genetic thing hiding in the genes just waiting to jump onto the genes of a foal.
Anyway, there are serious things to think about before a person should consider breeding and breeding a mare is nowhere close to a cheap endeavor.
First, you have to make sure that both the sire and dam have great conformation. A few minor flaws are acceptable, so long as the other evens it out, but there are some that are huge no-nos in breeding like calf knees, pigeon toes, extremely posty legs, super long backs, etc.
Also, the conformation of both sire and dam need to compliment each other. Generally speaking, if their conformation doesn't work well together, it wouldn't produce a desirable foal. That's why you breed cutting horse to cutting horse, jumping horse to jumping horse, dressage horse to dressage horse. I can't imagine the foal between a dressage horse and a cutting horse would be good for either of those disciplines. Plus, if it got just the wrong traits from each parent, you may end up with the fugliest foal on the planet.
Really, both parents should have proven themselves at some discipline first as well. Being sweet doesn't automatically qualify a horse as breeding quality, they need to be talented at something other than converting grass to poop.
Both parents need to be genetically tested to make sure that there are no genetic diseases like HERDA or HYPP or OLWS or any one of the other countless diseases hiding in there somewhere.
Each parent needs to have an amazing temperament because temperament can be genetic. If the sire is a beautiful horse with a rotten attitude, then you risk ending up with a foal with a rotten attitude who may not be so beautiful.
After the horse has been deemed worthy to reproduce, then you have to look at the costs to breed a horse.
1) There's the pre-breeding exam of the mare to make sure she's sound for breeding and having her tested to make sure she's not carrying any STD's (stud should be tested too)
2) There's the breeding fee itself
3) There's the numerous ultrasounds and vet visits during the pregnancy to make sure the mare isn't carrying twins and then to make sure everything is progressing nicely and the mare and fetus stay healthy.
4) There's the potential risk of the foaling, in which you could lose the mare, the foal, or both. If something goes wrong and you are able to save both, the vet bills from that would feed a small country for a week.
5) Then there's the immediately doubled feeding costs, farrier costs, vet costs, boarding costs, and training costs.
You also have to consider whether you honestly have the capability to train the foal. Let me tell you, training a foal is difficult. I'd been training older horses for about 10 years before I had my first foal experience and it was challenging as hell.
Then, there's the wait time. You're looking at 3 years before you can ride it, and that 3 years is a very long time when you're anxious.