Jonathan Burke gives an overview of the debate concerning the presence of domesticated camels during Abraham's time; notes that recent discoveries "has caused some scholars to reconsider the Biblical narrative."
Jonathan Burke, Living on the Edge: Challenges to Faith (Reference Work Series 1; Lively Stones Publishing, n.p., 2013), 198-202
Were camels domesticated in Abraham’s time?
WF Albright, one of the most famous 20th century archaeologists, argued that the camel was not domesticated until around the 1st millennium, well after the time of Abraham. This was considered persuasive by many Biblical scholars, who were convinced that references in Genesis to camels in Egypt during the time of Abraham are anachronistic. Some evidence alleged for very early camel use in Mesopotamia has proved dubious, but Albright overlooked evidence for camel domestication reported by the French archaeologist Petrie in 1907. However, Petrie’s evidence for camel domestication during the Ramesside era in Egypt (1292-1069 BCE), was still too late for Abraham (from around 1900 BCE), though significantly earlier than Albright’s date.
Evidence for early camel domestication elsewhere in the Ancient Near East and North Africa is well documented, and has been used to defend the Genesis account. It is recognized domesticated camel caravans must have passed through Egypt at an early date, though the Egyptians did not refer to them at this time. Bulliet observes that evidence for the early domestication of the camel in Mesopotamia cannot be ignored on the basis of their absence in Egyptian evidence. He agrees with Albright that evidence for Syrian domestic camel use during the 3rd to 2nd millennium is absent, and argues the undisputed evidence of their use elsewhere in Mesopotamia indicates they entered the area on a very small scale as pack animals by rich traders, rather than being herded in large numbers.
Firm evidence for very early camel domestication in Egypt has caused some scholars to reconsider the Biblical narrative.