How do I implement accurate distance measuring (to ground) on a plane-like UAV for heights over 10m?
You are probably looking for a radar altimeter, but I think that 1000m height will be a challenge if you want to build it yourself, because of power required to get detectable reflection at such distance. Couple hundred meters may be more realistic target for home made low power radar.

Here is schematics of radar landing altimeter that is usefull to about 1000 feet.