The only thing you need to copy over to avoid needing to redownload the blockchain is the blocks directory, everything else will be automatically regenerated (except the wallet; if you want to use the same one instead of using a separate one for the other computer, copy wallet.dat as well). If you're moving everything to a different computer and keeping the same wallet, you can copy over everything and it shouldn't need to reindex (saving you ~30min-2hr, depending on your computer). There's no "detatch" command necessary, but Bitcoin-Qt should be closed while you're copying the files.
I've always copied over chainstate... so you're saying you don't need to copy over chainstate on a --reindex?
Correct; the chainstate DB contains data about unspent transaction outputs, and is rebuilt when you run a --reindex (see https://en.bitcoin.it/wiki/Data_directory#chainstate_subdirectory). I'm not certain if it just applies to the wallet or to the entire blockchain, but judging by its size (and by how full nodes work) I'm guessing the entire blockchain. In that case, my earlier post is incorrect, and you should always copy over the chainstate folder as well to avoid needing to reindex; however, if you don't, it'll just rebuild when you first start the client. Since it doesn't need to download anything and is only using information from the blocks DB, it may take a while depending on your computer but it isn't dependent on network speed.
