Traders from Arabia travelled to and traded with Roman and Asian empires and this Nabataean Sea Merchants article. How far did Arabian traders travel - where was the furthest extent of their expeditions, particularly in Asia (or maybe Australia)?
It's not a full answer, but if you're interested by medieval Arabic travels, the unavoidable reference is Ibn Baṭūṭah. In his Rihla, he describes three travels he made during the 14th century :
- from Tangiers to middle-East, with a travel along the East coast of Africa, down to Zanbar and Kilwa. (map here)
- from Mecca to Beijing, and back, through Eastern Europe, Central Asia, India and South-East Asia. From the way you phrase your question, it's probably the travel which interest you more. (map here and below)
- from Mecca to the Mali Empire and back. (map here)
This text has been translated in many languages, so you probably can find a version in your preferred language. There is a French translation in la Pléïade, and a 19th French translation freely downloadable at the Université du Québec à Chicoutimi; I haven't found (yet) an English translation available on the web.