I'd like an analysis of Robert Frost's poem "Peck of Gold." What's the relation between dust and children, gold and children?

Robert Frost's poem "Peck of Gold" looks back at his childhood in San Francisco and focuses on the dust that seemingly covered everything. In the poem, he uses the dust as both a symbol of the historied gold rush and a symbol of childhood innocence. 
Frost opens his poem by explaining how much dust there was in San Francisco. He says it was "always blowing about the town," except for when the fog rolled in and cleaned the air of it. He explains that adults told him—as well as other children—that it was not just dust. It was also gold.
The Gold Rush in California began in the mid-1800s, according to the California Department of Parks and Recreation. The Gold Rush had a major effect on the population of the state. It went from 14,000 nonindigenous residents in 1848 to 250,000 in 1852. All those people settled there to find gold. This became a major part of California's history. 
By the time Robert Frost was born in 1874,  the effects of the Gold Rush were less immediate. People had begun to lead lives in California that were not entirely focused on finding gold. Its history and mythology, however, remained. This directly impacts the content of "Peck of Gold."
The dust and gold in the poem are conflated so that the children believe a negative part of living in California is actually a positive thing. He says, "Such was life in the Golden Gate/Gold dusted all we drank and ate." Even though they lived in negative circumstances, the adults encouraged them to see them as positive circumstances. That is why the adults say to Frost and the others that "we all must eat our peck of gold."
The dust can also be seen as a metaphor for childhood because it is given a magnificent value that does not maintain its power as age brings wisdom. Only a child would believe that dust covering everything is something magical and valuable like gold; once that child is older, they recognize dust for the nuisance it is. Before the loss of innocence, however, they are able to take something negative and make it a positive.
In some ways, the previous statement can also be read as a metaphor for the Gold Rush itself. For a short time, everyone in California was obsessed with gold. Like childhood, it was a short time of wonder and excitement for many. Once things changed and people realized there was not unending wealth in California's hills, they had to accept reality and move on to other ventures. In the same way, Frost and other children would eventually have to accept that the dust was not gold—and start looking for other things to improve their circumstances. 
https://www.modernamericanpoetry.org/dashboard

https://www.parks.ca.gov/?page_id=1081