No, it shouldn't reset. It's an "aged" Roth, so they should see it that way (but confirm with Vanguard). I transferred several accounts from several different financial groups early this year, and all of them were considered the same. At the worst, you'd keep the paperwork showing the contribution dates in the old account and a copy of the transfer into the new if they can't confirm.
I transferred to Fidelity, and what they had me do was open an account (same type of account as what I was transferring), then they had an account number to work with on their end to transfer the funds into. Then I filled in the paperwork, turned it in to them and they handled the transfer after that.