She also helped to take the team of Jamie-Lee Wright, Helena Duguid, Danielle Hanley and Karina Jackson to a team gold.
'That was my big goal coming into the week, I'm absolutely over the moon,' she said.
'That was pretty special – the crowds were incredible, with so many people cheering.'
Brehaut's father Paul took silver in the men's event 20 years ago.
Guernsey has also claimed more medals in cycling, with team silver for the men of Marc Cox, Matthew Osborn, Jack Reed, Alex Van Katwyk and Sam Culverwell, who took individual silver.
More gold on the shooting range too, from Ollie Hudson and Nicholas Kerins in the Fullbore Kings Pairs, and there was silver in the men's 10m air pistol team event for Paul Guillou and Jack Hanca, and for the sport trap team, from Ross Angus, Clifford Eborall and John Wild.
Further updates to follow
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