Yep, you treat them just like onion seedlings. I have grown both of those varieties with good results. One year I did have a little bolting, so I wait until the soil warms a bit in mid-April to set them out. In my experience, the seed-sown shallot varieties grow a little stiffer than bulb onions, and are slightly easier to handle. We're eating last year's crop now. They store forever.

Would a 1/2 gallon cardboard milk container work? If so how many seeds would you use in it?

1/2 gal. cardboard milk container is too deep with little surface. Onion/shallot seedlings would nee no more than 3" deep soil.
Although you can cut away top half and use the bottom, but then you cannot plant very many seeds in it.
JMO

I tried to buy shallot seeds at our local garden center. They did not have any but said they were coming in soon. I'm not sure if they meant the shallot sets instead of seeds. My question is - are shallot seeds hard to find?
Helen

shallot seeds can be hard to find, but I think I saw them in johnnies catalog. they did have free shipping earlier.

I was also wondering about how to find shallot seeds.
The thing is that there is no (or very tiny) demand for shallot seeds and that is why it is not marketed like onion seeds. This year I will let some of my shallots to produce seeds.

I mail order my shallot seeds from Johnnys, and a few other seed suppliers have them, too. I think they were bred in the Netherlands. The seeds keep for me for three years, which is how long it takes me to use up a packet, growing one flat of 75 per year.

Another question to Planatus:
When you plant seeds, do you get good size shallots the same year ?

My vegetable garden is scattered with all types of shallots. Last year I grew from seed direct sown (Johnny's F1 hybrid Picador and Saffron), and they did okay, probably half the size they should have been and probably would have done better with better conditions. One bulb grows for each seed planted. The shallots I grew from seed kept amazingly well for about six months. I don't think true shallots go to seed. Johnny's is all F1 hybrid seed. I will probably never sow shallot seed again once I use or give away the rest of the seeds I have. This year I put seed grown bulbs back in the ground to see what happens for vegetative reproduction along with 'true' shallot types like french grey and red shallots. And I'm taking advice that they are effective garden companions to repel unwanted animals and insects, so they get to live with strawberries, spinach, etc.