When I showed my kids (5 & 2) what we could do with our 3D printer, the first thing they asked was if I could print them their own 3D printers. It took me 6 months to get around to it, but I finally managed to finish this design. It is roughly inspired by a well-known 3D printer, with a lot of small changes to make printing easier.
When I gave it to my son today, he came back an hour later and said "look, I 3D printed a sock!"
The file is 5cm tall, but works all the way down to 3cm. See the Instructions tab for printing details. Designed in Auodesk Fusion 360. The F3D archive is included if you want to tweak the design, and so is a version with meshmixer support.
I have printed several times at 5cm and 3cm high on a Replicator 2, at medium defaults (0.2mm / 2 shells / 10% infill). Takes 2h30m for 5cm, and about an hour for 3cm.
I printed vertically, with meshmixer support (tried makerware support but it was impossible to get out from under the print bed). It is not "stock" generated support, I made manual tweaks, and even used the sculpting brushes to grow the bottoms of the posts under the bed a little bit, as sometimes they get knocked over by the print head. I use small needle-nose pliers and a dental pick to get the support out from under the bed. And a razor knife to slice off the ears (otherwise my print warps).
However, it now occurs to me that it might be possible to print it on its back, and avoid most of the support!