Short and a little simplified description of my trip: 
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Peaks at begin/end: Flights Munich-Doha and Doha-Dar Es Salam (and 
back, at 12.5 km altitude), 1. day after the first two peaks: Dar Es 
Salam (50 m), 2.-3. day: Moshi (900 m), 4.-8. day: Climbing the Kibo 
(a volcano which is the highest peak of Mount Kilimanjaro, via Machame 
route with Vulcan tower, Uhuru Peak (5895 m) at the morning of 14.7.), 
9.-11. day: Moshi (900 m), 12.-13.day: Dar Es Salam (50 m). The days 
are simplified counted from noon too noon.  
The X-Ray-Checks at the airport check-in can be seen as little peaks.
The approximate route profile at the Kibo can be found at
http://www.zara.co.tz/kilimanjaro/i/macprofile.gif
There seem to be two reasons why the Uhuru Peak dose rate is a little 
reduced and noisier: a) the low temperature (about 0°C at the gammascout)
and b) to avoid freezing the gammascout was in a bag close to the body;
the body shielded a little more.
Conclusion: 
The dose rate in µSv/h near the equator is about
0.15 +0.133*(altitude/km)
and at a latitude of about 48° it's about
0.15 +0.3*(altitude/km)
in a heigth of 0 to 12.5 km. 
From flights close the north pole i know that the poles the rate is about two
times highter as at 48°.
Near the equator the increase is linear from 0 up to 12.5 km. At higher
latitudes the increase is stronger and non-linear. 
This must be caused by the soft component of the cosmic rays which is shielded
by the earth's magnetic field at the equator.
This makes sense because the lower energy cosmic rays are shielded stronger by
the earth magnetic field and explains both a) the lower cosmic ray intensity
at the equator and b) why the increase with the altitude is linear at the
equator and nearly quadratic in central Europe/USA.
See also
http://www.ptb.de/de/org/6/64/flugdosis/hoehenstrahlung/hoehe.htm