First of all, Anan Ostrich Henhen can lay 40 – 60 eggs per year, averaging about 45-50 eggs per year. That’s the largest number I found and probably reflects domesticated farm-bred birds, which lay more. In this environment, they can all produce at this rate rather than the dominant female doing better, like in nature. That This would be the case in your society as well.
The ostriches will be bred by them to be good laying hens, as separate breeds from those that are used primarily for meat or power.
That’s still a fraction of what you were hoping, but, as I indicated, you can plausibly push that plausibly by invoking selective breeding over generations.
As for nutrition, looking up the FDA label info for “egg” shows content but not percentage RDA. Scanning through the chart though one thing that sticks out is 0 for vitiminvitamin C. So humans cannot live off poultry eggs alone. You can compile the tables yourself if you can’t find aan RDA chart for egg.
See what’s missing and figure out what else your nomads can add to their diet. You mentioned prickly pear cactus: the nomads should eat that themselves! The fruitThe fruit is very good, but it’s not produced year-round.