Is it normal for my 8yo to begin showing pubic hair?

Can be normal . In girls is accepted the presence of hair after 8 yo.
Likely, yes. Some children can have early adrenarche/pubarche and so develop pubic/axillary hair. But other more 'serious' causes need to be ruled out.
Can be normal . There is evidence that appearance of some pubic hair as early as 6 yo is normal in females. Minimal circulating hormone may produce this change in isolation. At a regular checkup a review of the growth rate and any other features of puberty can be evaluated. Some populations begin the transition into puberty as young as 8, most girls wait till 10 and boys 12.