Yes you can give your kids a popsicle for breakfast! Try this Breakfast of Champions: A frozen banana that has been dipped in yogurt and then rolled in Cheerios! This site also have several more healthy and EASY Popsicle ideas :)
Baked Banana Chips - toddlers love these! Slice bananas very thin (1/8"), brush with lemon juice mixed with just a little water, sprinkle with cinnamon and kosher salt. Bake at 250F for about 2 hours, turning after 90 mins. Let cool (the longer they cool the crispier they become). Smear a little peanut butter between them if you like. Perfect sweet little treat! Enjoy!