How do I organize a shared bedroom for a toddler and infant?

If possible give each child their own space. You could divide the room to make two 7.5X10 spaces and perhaps put a curtain between the two parts. Depending on sex of children you may be looking for a larger place later and the curtains won't leave much to repair before sale.

It's a good size room so you should be able to give them separate sleeping areas. I would put them on opposite walls staggered, with the infant closer to the door. Make a play area for the toddler in on corner and put a bookcase and glider to sit and read to them in another corner.

Or in place of the curtain, you could put bookcases back-to-back to create a wall and also provide storage space for books, toys, etc. I'd use 6' bookcases to maximum storage and privacy. Be sure to anchor them well, perhaps through the backs.

love the bookcase idea. an alt (less expensive) way might be a sheet of insulation board. It can be painted and wedged between 2 pieces of furniture (chest, dresser, etc) to provide a "half wall"

Babies don't take up that much space so just do a neat corner for the infant with their crib and changing table. Then do another corner for the toddler so they each have their own space. Then bring the rest of the room together with a reading nook and play area so they can grow together because babies grow fast. Use the closet to organize their clothes and all the other things that come with having young children.