Pens for Calligraphy
According to Mandel Kahn, the only proper instrument for Arabic calligraphy is a calmus reed, modern Arabic calligraphy sources recommend a standard western style calligraphy pen1. Looking at Levy’s translation of Ibn Badis’s manuscript on calligraphy and illumination (written in 1609), most writing was referenced to a reed but both brush and feather were listed as suitable for writing. “The part of the wings of eagles, thick with feathers, is taken. From it, the hard thick place is chosen and the quill plucked. The pen is cut off with scissors since the knife does not do it entirely straight. A short cut is made for the pen. The fat is removed from it to make it thin. It is good for drawing and writing.2”
Weather one chooses a feather or reed, the cut made is much the same. (insert instructions here) While no mention is made of it in the period texts, I've found having some wadding (silk, cotton) or a curl of feather shaft or wire inserted into the tube of the pen will allow it to hold a larger drop of ink and thus require fewer visits to the ink well.
The brush is frequently mentioned in calligraphic texts, though I am assuming that it was largely used when producing calligraphy in painting rather than as text.
1Oureshi, Jafar H. in Arabic Writing for Beginners recommends modifying a fountain pen by flattening the tip. A standard calligraphy cartridge pen would be a similar solution.
2Levey, page 38, page 39 discusses the use of a brush for calligraphy.