My phone is also too dump store a timestamp into an EXIF header, it doesn't even create an EXIF header.
But I've found a way around this, if you are using Linux (or some other flavour of *nix):
use
cp --preserve=timestamp
to copy the pictures from the phone to another directory
Then use
jhead -mkexif -dsft
to create an EXIF header with a timestamp based on the file creation date.
After that you can use the tool of your choice (I use gpsPhoto) to geotag the pictures.