Font with Phonetic Arabic

I am a historian, and not an expert in fonts, but I am frustrated. I am looking for an English font that has the equivalent phonetic letters to Arabic letters. Eg. A heavy T with a dot under it, a dhall or d with a line through it, etc. Is there a font similar to Garamond (for publishing purposes) that has all of these characters?

EG: Sa’īd Ibn Ḥusayn changes his title to Imām ’Abid Allāh al-Mahdī Billāh.

I find myself using multiple fonts to find all of the different characters I need. Is there one font that has them all? Perhaps an Arabic font that contains them? I prefer to purchase it so that I can use it regularly.

Phonetic font suggestion for Mac

I have received a Word doc from a client with a word displayed in a phonetic alphabet font (see attached sample). I can't seem to find a font on my Mac OS 10.6.8 running InDesign CS 5.5 that will match the characters. I would have thought the OT version of Minion Pro, for example, would work, but no joy.

FWIW the font used in Word is listed as HiraMinPro-W3, which to me indicates it is at least sourced from Minion Pro. Maybe I'm just a gumby and can't activate the required set through the Open Type dialog in InDesign?

Any suggestions?