When our son was a toddler he did get a room key for the FOTL. At that time only one person in the party had to show the key to get the FOTL access. There are rides, such as ET, that young children can go on that FOTL would be needed for.
We kept our room keys (and Fastpass tickets at WDW) in a little credit card holder. I've seen them at Wal-Mart, etc. in the wallet section of the store. It was a good system at WDW because we were able to put our fastpasses in the section with the clear window and could easily check to see what time we needed to return to ride.