Peer review doesn't, and hasn't ever, included replication of the experiment.
Uno
Publishing the methodology, statistics and results allows others to analyze the data. That is peer review.
No one gives a shit about 1 experiment/study. Ever.
Eggs cause heart attacks!
Eggs protect from heart attacks!
Eggs have no discernible affect on heart attacks!
Hence, the same methodology will be used by other researchers, which is how you determine if the actual results are worthy of adding to the knowledge base, or throwing away.
First, you publish your data in a journal where peers review the data.
Second, it is replicated by others, or it exists as simply one study that no one gives a shit about.
I'm sorry that I skipped over the middle part. But yes, replicating the experiment/study is part of the process, assuming that anyone gives a shit about the original experiment/study.