As Ethiopian does not serve Algeria, this looks like you bought a ticket with a combination of Ethiopian and Egyptair operating your flight. As animals generally are never interlined between airlines, you will need to claim him in Cairo , go landside and pass immigration/customs/agricultural inspection there before you can check him in again with the carrier that operates the onward segment.
This will in all likelihood turn out to become a nightmarish experience with various Egyptian authorities. I had to cancel a trip to there after over the course of several months I was unable to establish how to get my (service) dog into Egypt.
I would strongly advise to abandon this plan and do the following, in the order of preference:

- change your flights so all segments are operated by Egyptair. That will enable you to check the animal through to your final destination and avoid all transit hassles. Be aware that Egyptair has a 45kg weight limit (dog plus carrier combined) for animals as checked baggage. Find their pet policies here.

- Change your itinerary to one that will use just one airline with one stop: Options are Turkish Airlines via Istanbul (this is likely what I'd do, TK is a pet-friendly airline), Qatar via Doha and Emirates via Dubai. Here as well, the animal can be checked through. Compare layovers - timing and duration. You want the layover to be as short as possible, and during cooler phases of the day.

- ship the dog as manifested cargo with either of the above one-stop carriers. This will be substantially more expensive but probably the best solution.

BTW, this thread would probably be better placed in the 'travel with pets' forum.