Unlike other farm animals in Stardew Valley, you can't buy baby ostriches from Marnie. You'll need to travel to Ginger Island to get your chance at receiving an ostrich egg, which is possible after you've finished repairing the old boat in the back room of Willy's shop (which in turn is a quest unlocked after completing the Community Center or the JojaMart Community Development Form). One trip to Ginger Island costs you a fee of 1000 gold, but paying that fee won't be necessary anymore once you buy the Island Obelisk from the Wizard.
Once you arrive on Ginger Island, there are two ways to find your first ostrich egg - an easy and a more difficult, luck-based way:

1. Pray to RNGesus when looting chests in the Volcano Dungeon. You can find the Volcano Dungeon in the northern part of Ginger Island. There's a chance that the chests inside the dungeon may contain an ostrich egg, but honestly since this method is based on luck and RNG, so tbh I wouldn't consider this a 100% guarantee of getting an ostrich egg as fast as possible.

2. Find the journal scrap #10. Journal Scraps work the same way as the Secret Notes, and give you information about special locations on Ginger Island. The journal scrap 10# indicates a special spot on the island where you have to dig into the ground to receive a Golden Walnut and your first ostrich egg. This is the easy way to receive your first ostrich egg. Now it's time to find out how to hatch your first ostrich!

Note that ostrich eggs cannot be put into the usual egg incubator that is used for chickens, ducks or dinosaurs. To receive the possibility to hatch your ostrich egg, you have to finish the quest revolving around Professor Snail and his Island Field Office.
Professor Snail is a NPC stuck in cave on Ginger Island. Once you find him and are able to free him with the help of some explosive methods (bombs), he'll give you the task of completing a small museum collection. If you complete all four fossil collections and answer the questions he has for you correctly, he will reward you with the Ostrich Incubator recipe. To craft the Ostrich Incubator, it requires 50 Bone Fragments, 50 Hardwood and 20 Cinder Shards. When you've crafted an Ostrich Incubator, you can place it in a barn on your farm.
Once placed in the incubator, the baby ostrich takes around 9 days to incubate (if you have the Coopmaster Profession, this incubation time is cut in half). If the birds have enough to eat everyday, the baby ostrich will mature into an adult ostrich after 7 nights and proceed to lay an ostrich egg every 7 days. You can keep those first eggs and put them in the incubator in order to increase your ostrich population.

Short answer: Yes. The selling prices for ostrich eggs are as following:


When you put an ostrich egg in a mayonnaise machine, one ostrich egg produces 10 jars of mayonnaise of the same quality as the egg itself - this is the huge, money-making difference between ostrich eggs and normal chicken eggs/duck eggs. As you can see, I collected three normal quality eggs, one silver quality egg, two gold quality eggs and one iridium quality egg in my barn.
FIY I currently have the Artisan profession that grants Artisan goods to be worth 40% more, so after putting one iridium quality ostrich egg into the mayonnaise machine, I received 10 jars of iridium quality mayonnaise worth 5320 g.
Ostriches are not the most lucrative farm animals in the game, that #1 spot still belongs to the pigs. And before you can start to raise your first ostrich on your farm, you'll need a lot of time and resources to unlock Ginger Island in the first place. But they are a valuable and cute addition to your farm, so I'd definitely recommend having at least two ostriches on your farm if you have the space.