Records from tombstones in Laurel Hill Cemetery from 1853-1927.
Compare the listing for Willie Howard Bee to the dates in the newspapers listed below.

The 1852 California State Census listed Frank M. Bee as the only child of Frederick Bee.

Daily Alta California, Volume 6, Number 286, 16 November 1855
Death of Willie Howard, son of F. A. Bee –about two years of age – at Placerville

11-10-1855 Willie Howard Bee's death
Article that mentioned gravesite

From November 17, 1855, Mountain Democrat, page 2
In this city, Nov. 10, of croup, after an illness of two days, Willie Howard, son of F. A. and Catharine M. Bee, aged
1-year 10 months and eleven days. San Francisco papers please copy.
Oh, Willie, Willie, Willie dear!
Oh, do not leave me: oh no;
My heart so longs to keep thee here,
'Twill break to let thee go.
They say thou hast a blest abode,
And bid me not to cry,
I know that thou art gone to God—
An Angel in the sky.
But, Oh. the earth, it lies so cold
And damp upon thy breast.
I feel as if my arms must hold
My darling in his rest.
It seems as if his spirit still
Were lingering with the clay,
As if that little form were chill,
In that dark place to lay.
Oh, Father of the good and blest,
My darling baby keep;
And may I find his haven of rest,
When I shall fall asleep.