First of all, [An Ostrich Hen can lay 40 – 60 eggs per year, averaging about 45-50 eggs per year](https://www.ostriches.org/about-ostrich/faqs).  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 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 push that plausibly by invoking selective breeding over generations.

As for nutrition, [looking up the FDA label info](https://ndb.nal.usda.gov/ndb/foods/show/112) 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](https://en.wikipedia.org/wiki/Scurvy).  You can compile the tables yourself if you can’t find a [RDA chart](https://en.wikipedia.org/wiki/Reference_Daily_Intake) 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](https://en.wikipedia.org/wiki/Opuntia_ficus-indica) is very good, but it’s not produced year-round.