The phrase “right as a trivet” means: Absolutely right; right as rain; all hunkydory; all to the mustard.
Inasmuch as a trivet, a stand for supporting vessels in a fireplace, was always three-legged in former times, the housewife could set it anywhere upon her hearth, certain that a pot thereon would rest securely.
The expression began to appear in literature early in the nineteenth century.