A taxi for the whole 100 miles would be very expensive and take 3 hours. The bus trip is reasonably straightforward but will take you much longer than you think. As Carol says, taxi or dolmus from Dalyan to Ortaca from where there are regular buses to Fethiye about an hour and a half and then from there a bus to Kas (hourly) which will take you another 2.5 hours.
There are direct buses from Ortaca, ie Pamukkale at 16.30, KamilKoc 16.35, maybe others, very comfortable and cheap at 28TL.
It leaves Kas from In front of the Lycian Property near (YapıKredi & the old Mosk) shared transfers to Dalaman Airport are being offered for 50 TL.
They drive every day at certain times.
Kas to Dalaman: 05:00 / 09:30 / 14:00 / 18:30 / 20:00
Dalaman to Kas: 08:30 / 13:30 / 18:30 / 23:00 / 24:00
Here's a link to the homepage: http://www.lycianproperty.com/transport.html
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