If you're okay with piecing a few parts together here's what I'd do:
1. Get a 3xCR123 P60 host and run in with 2xAA batteries (you can make or buy a spacer if you don't want them to rattle).
Examples: Low price - Solarforce L2 with L2-E18 extender. Higher price: Surefire G3 host from Oveready.
2. Get a low voltage P60 drop in.
Examples: Low $ - Solarforce low voltage drop-ins. Med $ - Nailbender / customlites.com P60/D26 XP-G2 low voltage. High $ - Malkoff M31LL; this is also lower out put, and longer run time.
3. Get a diffuser or lantern kit. There are many low cost options.
Examples: My favorite is the Xeno safety wand. The Solarforce L2-DW is a package that comes with both white and orange wands, so it might not be a bad idea either. The Solarforce LT-1 lantern kit is worth looking at as well. It might be a little bright without wrapping in come colored plastic or diffusion film to further attenuate the light, but it will provide the most light bulb like light pattern. The included stand also gives the light a very stable base.
There are several advantages to going with a P60 host. First, it's the de facto standard for flashlight modding, so there are plenty of accessories to customize it and get it just how you want it. Another advantage is that as your child gets older and more responsible the light can grow with him by simply changing out the P60 drop-in to a brighter one and/or removing the diffuser. Finally, if there is a houeshold emergency even his night light will be a quality light that can quickly be pressed into service.
If you want to go with a factory light I'd get a FourSevens Quark Tactical single AA (model QTA) and just program both modes to low (4 lumen) or one mode to low, and the other to moonlight (0.2 lumen). If you're still worried about it being too bright I found
this thread over in CPFM indicating that the Fenix traffic wands and light diffusers will either work on the standard FourSevens bezels as is, or will work with a little sanding on the inside of the wands / diffusers. The ability to program to the FourSevens light to various output levels, plus the fact that they sell just the heads to screw onto existing bodies makes this another light that will be extremely versatile in terms of immediate and future use.
I hope that helps.