Rather than trek to Kilimanjaro which must be a few thousand miles, I would take a plane and then just climb the mountain!!

There are two climbing seasons for Kilimanjaro, mid December through to mid March, and early June to mid October which are known as the dry seasons. Mid December through to mid March tends to be dry and warm, whereas June to mid October is generally cool and dry. The most popular season is generally the warm and dry season particularly around Christmas.

Here is a link to a very useful guy I have used in the past who help me organise treking in Nepal, but he also covers Kilimanjaro:

http://www.themountaincompany.co.uk

He's on skype and will help with all aspects of your planning.