Spay/neuter or leave intact, and when, ... all the data isn't in. I think you need to really read the research and make your own decisions. But I certainly would wait until 2 or 3 or not at all. And realize even then, both can have deadly consequences. IOW, it's your dog and choice as you'll be the one carrying the loss if it goes bad.
My big concern for long cycles is pyometra. The longer the cervix is open, the long bacteria has to enter and cause an infection.
Have you talked to your breeder? Seems like she should have told you. Call and ask.
Please check the Basenji Club breeder's list:
Sadly, most isn't exaggerating... it is fairly realistic preparation. If you need an easy dog, a dog that is easy to train, on that won't challenge you or look for alternate ways to do what you said literally without actually complying, this isn't the dog for you.
The upside: Waking up to sayblee's nose gently touching mine to wake me up. The "not dog" smell. They eye contact and feeling of companionship more than a pet. Watching the cogs turn as they figure things out. Gaining their trust and love so they are willing to work with you.
Consider fostering one for a few weeks up to 2 mons and get a close person view of what it is like.
There is NO BREED OF DOG ON EARTH that is hypoallergenic. Period.
I totally disagree with "keep the dog outside" but the rest may help. Try being around the dog or several. See how you can tolerate it.
I am glad to hear of her improvement. Sometimes we live with dogs and don't see the changes they start so slow. It's good to make it a habit to actually inspect them monthly. I hope she keeps improving but as Sally said, too much weight gain isn't good.
You could do a DNA test to get some ideas. I don't see Basenji, but I've seen mixes that the bitch is known to be one breed and the pups don't look like they could be related to her. Your dog looks like a small Lurcher, but that's probably the terrier I'm connecting with. Whatever, that's one happy dog.