I've always tended to be a person who did as much for my pets as possible, even at significant personal cost, if there was a reasonable chance of decent quality of life. I've also done fostering for out local Humane Society, and known people connected with several other rescues. Plus I just know a lot of people with pets! Ultimately, you are the one with access to information about your dog's health, prognosis, quality of life currently, etc. So you're the only one who can decide what's right for her. But I'd hate to see a young dog put down because of what might develop down the road. Here are some pertinent thoughts/examples to your situation:
"My" first dog (as an adult) had obviously torn her cruciate ligaments when younger, and was not treated. Yes, she had arthritis (but then, she was a middle-aged dog when I adopted her), and she was a pretty big girl, about 80 lbs. Sure, the arthritis had some impact on quality of life, which I would describe as aging her faster, but we were able to give her some relief with medication, and I would not have said that she needed to be put down for that reason. She loved to walk and walk and walk, and we put in a solid 1.5 hours a day at a good clip, right up until close to the end. (And I lost 2 pant sizes in the first 6 months I had her!) She'd be creaky first thing in the morning though! She eventually developed a condition called ITP, and when she didn't respond to treatment, was euthanized then.
A friend's dog, a very active golden retriever mix, had cruciate surgery on both legs, with the whole "6 months cage rest/only out in the backyard on a leash to pee" thing. As startingsmall says, the activity restriction could be helpful even without the surgery. It's not as bad as it sounds! It would require you to have a decent size cage (big enough to turn around and fully stretch out), plus do things to provide the dog with mental stimulation. Chew toys, puzzle toys, brushing them, teaching them tricks, etc. They aren't necessarily in the cage when you're home, by the way, just when you're not around to supervise their behaviour. Molly (friend's dog) didn't love this period of time, but she survived it, and is happy and healthy now (years later). Actually, because they had to work harder at engaging her mentally, and training her to go lie down rather than jumping around, I would say she became better trained during that period of time :-)
Many rescue groups would absolutely be happy to take your dog and treat it, if you feel you can't or won't be able to treat her medical needs in future. Finding one that has the room and ability to do so at this particular juncture in time is the tricky part! Because many are currently full up with other dogs that they're doing the same thing for. But you may be able to find one that will take her eventually, if you can keep her until they have an opening in one of their foster homes. Best bet, if she is any particular breed (doesn't even have to be an exotic breed) is to look for a rescue group that specializes in that breed. Some breed specific rescues will take in mixes of that breed, and there are also some semi-generic rescues, such as ones that specialize in small dogs overall. Also, ask them to cross-post it/put it out to their networks if they don't have the space right away. Lots of animals get placed via facebook, even out of area, and sometimes they can even help arrange transport.
One example of a rescue group going all the way for an injured animal. Our local humane society had a vet volunteer to do surgery on the badly broken leg of an 18 year old cat that was surrendered to them, putting in pins so she could recover - after they did an exam and blood work to ensure she had no other major issues. They ended up deciding she wasn't highly adoptable, so she ended up in a foster home - mine! Where she happily lived 3 more years, and died peacefully at home at the ripe old age of 21. When I adopted one of the other cats I fostered, I mentioned during the pre-adoption vet check that his breath was foul. They had a vet doing volunteer work to get a dentistry specialization, so whisked him off to be seen by her. He had all but two teeth pulled in the end, and a very fancy "case study" report produced! I know I've strayed pretty far from the original question with these last two examples, but my point is that it may not cost the shelter/rescue group as much for the surgery, because they may have their own staff vets, or get a discounted rate from a vet they work with regularly, or even have a vet volunteer to do the surgery. It all depends on the shelter. This is not as likely to happen in a city-funded shelter, but may be possible at one of the shelters or smaller rescue groups supported by donors.
Hope this is helpful, and I really wish you luck in determining the best course of action for your situation.