Turbah is the best thing to perform sajdah on. If not available then any naturally grown substance which is not eaten or worn can be used for sajdah such as leaves, grass, stones etc
If your toddler will take the turbah you have to hold it in your hand and only put it down when you are doing the sajdah. It is not allowed to do it on the mat (unless the mat is made straw etc) nor is it allowed to break the namaz.
At Airport or friends house one can use white paper to do sajdah or keep a small turbah with them.