I've been Family Sharing my Rust account from my old account to my new account for about a year now, and during this time I have gained achievements and over 1000 hours of playing time on my new account. I know I will keep the achievements if I buy Rust on the new account, but my question is, if I buy Rust on my new account, do I keep the hours I've gained from sharing? I would like to keep my 1000 hour history.
This is not possible: playing time is exclusively tied to the user having accumulated it.
As far as Steam is concerned, your two profiles are completely unrelated, even if connected through Family Sharing.