Where can I find LDraw files to download for basic figures? I would like to have a collection of simple examples for my youngsters.

Only for basic LEGO bricks. Not Technics or complex and complete space stations, just some
step-by-step instructions for the basic bricks. Based on the starters edition from LEGO.

I was thinking of: houses, small animals, simple aeroplane, simple car, tree, ...
All based on the basic instructions.

This would help the children a lot in playing.

See the pictures. I would love to find step-by-step instructions in LDraw.
This answer will by definition have a lot of links, but here we go. Since you're looking for instructions there are a few sites that you should consider visiting. 

The first is Cubiculus, which specializes in creating LDraw versions of custom and official instructions. The creator of the site adds plenty of his own (basic) instructions.

The second is Rebrickable. It contains many creations by various builders, and some provide LDraw files for you to download. The instructions are usually quite advanced, however.

Lastly, you could put together your own LDraw files from LEGOs basic sets. The biggest consolidated collection of instructions is available on Swooshable. (Full disclosure - it's my own scraper that consolidates set instructions from the five biggest sources on the web. I built it to not have to check different sites for a particular instruction.)

Hopefully that'll get you on the right track.