Unfortunately, the Uighurs themselves did not arrive in the Tarim Basin
until nearly a millennium after the Han Chinese
(Victor H Mair)
Evidence of Han Chinese in Tarim Basin in 2nd c BC
(CP Fitzgerald, Anders Corr)
Uighurs resettled from Mongolia to the Tarim Basin in 840
(Wikipedia)
Loulan Beauty remains a mystery
Neither Sinitic-speaking Chinese nor Turkic-speaking Uyghur
What language did she speak?
Evidence suggests she may have spoken Tocharian,
the second oldest (after Hittite) Indo-European language
(Victor H Mair)