We have been to the Fezzan with our 3.5 year old daughter two years ago, it was a superb trip, all of us enjoyed it. The pace of the trip was much more relaxed than what we normally do, and we focused on leaving time for her to do the things she enjoyed - in a way the sahara was for her like an enormous sand box on the playground. Then again, she has demonstrated on previous trips (we have also travelled with her when she was 9 months, and 1.5 & 2.5, though not to the sahara) an exceptional adaptation to different environments, which may not be the same for all children.
However a year old toddler is a different matter, I would not do it. In the first year the little one is pretty much an extra piece of luggage, little affected by the environment, but needing LOTS of attention, that will pretty much spoil the trip even if nothing goes wrong. Folowing that they still sleep a lot, espacially in the car, and tolerate the heat remarkably well (all trips were to places with temp in the 35-40C range).
A major problem is in hot climates you have to change those diapers immediately when something gets in them to avoid a bad rash (or have nothing on,like local kids, which is much better, but that's not an option in the seat).
Additionally, under two little children have an alarming tendency to come up with varied new symptoms you've never seen before. You're no longer worried with the second child, but with the first you want immediate reassurance from the doctor that everything is all right - most of the time it is, but a few times it's more serious, and needs immediate treatment. (What do you do when all of a sudden your 1 year old has 40C fever 200 kms from the nearest town, a full day on those roads, and the only available doctor only speaks arabic and berber?)
I suggest you do the trip when the little one is big enough to enjoy it too, and go to some more tame destinations in the mean time.