First of all, An Ostrich Hen can lay 40 – 60 eggs per year, averaging about 45-50 eggs per year. That’s the largest number I found, and probably reflects that domesticated farm-bread birds lay more and they all can produce well as opposed to the dominant female doing better. That would be the case in your society as well.
The ostriches will be bread 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 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 vitimin C. So humans cannot live off poultry eggs alone. You can compile the tables yourself if you can’t find a 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 fruit is very good, but it’s not produced year-round.