I thought the OP had a registered QH mare, with good lines, good conformation and a great temperment that she(?) wanted to breed to get a foal with a bit of her in it?
I see nothing wrong with that.
I don't agree with "collecting" horses from rescues and breeding them, nor do I have any problem with rescues putting a non-breeding clause on the horses they find homes for (no different than the SPCA having their mandatory spay and neutering). Most rescues I've come across will only put limitations on horses who have a soundness issue when it comes to what they can and can't do for "work" - again, I see nothing wrong with this, as a lot of people who DO purchase (adopt... whatever you want to call it) rescue horses often don't know much about horses.
I don't totally agree with reiner's statement that it's "Cheaper" to breed a foal than buy one.
Here's some math :
Say you do AI to a quality stud... I'll go with a stud fee of about $1000 (because if you want a performance horse, the sires usually come with a stud fee around that mark... unless you're breeding to unknown stallions or young studs with no show career yet, either would be a "risk" )
Now, AI means you're going to need to ultrasound the mare (in my area this runs somewhere around $250 every US... NOT including the transport and/or board I may need to use until the mare is ready to be bred). Let's say it takes you 2 tries to get this - $500
After the insemination (or live cover breeding for that matter) you need another ultrasound for the mare - to make sure she's taken, the fetus is where it should be, there are no other problems etc.)... another $250 here
You have the feed and care the mare needs during gestation - probably varies depending on your set up and how much feed costs in your area. Runs me around $1200 a year for the feed, with vet costs/deworming/farrier care we'll say $2000 just for easy numbers - it's not really highballing either.
You may or may not choose to do an ultrasound later on in gestation - to check and make sure things are OK. $250.
As the mare gets ready to foal - we're going to hope that everything goes well, and you don't have any vet bills from the actual foaling... but they happen, and they can be VERY expensive. (just for argument's sake... this number is a variable every breeding... and lets not forget you can lose the mare and/or the foal at this point)
If we add all this up : $4000 .... which could be a conservative number or a high one depending on where you live, how much property you own, and if there were any complications anywhere along the way.
So that's $4000 to get the foal on the ground... as it gets older and you put time and money into care and training that goes up.
I've seen a number of breeders, of quality stock (let's face it a foal which isn't quality isn't going to sell for $4000 + at weaning) who offer foals for around this price... so you CAN find them, and still not be spending any more money than you might if you bred your own.
(This isn't me saying that you shouldn't breed your own quality stock... just pointing out that it really isn't "cheaper" most of the time to do so... or at least not signifigantly cheaper when you take in consideration the risks and possible bills you COULD get hit with if things go wrong)