Yes, DNA is copied before meiosis begins.
Before a cell can undergo meiosis, it goes through a phase called interphase, which includes DNA replication. This replication process results in each chromosome being duplicated, creating two identical sister chromatids. These sister chromatids remain connected at the centromere until later stages of meiosis. So, while meiosis itself doesn't "copy" DNA during its phases (meiosis I and meiosis II), DNA replication is a crucial preparatory step.
In essence, the copying of DNA happens before meiosis to ensure that each resulting daughter cell has the correct amount of genetic material. Without this pre-meiotic replication, the chromosome number would be halved in each successive generation, leading to genetic instability.