it actually seems to be the other way around. the semitic sumerian name for the goddess ishtar actually seems to be inanna, which is an etymology that is very different and actually comes from a semitic sumerian word/root. astarte/ishtar appears to be an indo-european word borrowed by the semites to describe a semitic sumerian, rather than indo-european, deity. it might have origins during one of the early indo-european occupations of mesopotamia, and there were several before cyrus, some quite ancient.
so, easter is not derived from ishtar, but ishtar appears to be derived from the same word as easter.