Build a toddler size tee pee bed using the free woodworking plans at the link. It is an easier project than you might think at first.
Build this simple twin bed using this free step-by-step tutorial. Plan requires only off the shelf lumber and minimal tools.
Why build a basic bed when you could build this house frame toddlers bed. This one is sized for a crib mattress but you could adjust the width and length to fit a single bed too. Free plans at the link.
This beautiful toddlers bed was built using the dimensions of a crib mattress. Follow the free step-by-step plans at the link to build this bed.
This is a link to a Google 3D SketchUp drawing for a toddlers bed. Uses standard boards (mostly 1x6s). You will need the SketchUp software to download this drawing and its freely available online.