Thank you for your quick reply...my daughter was so excited and immediately started doing handstands (she does not lack in enthusiasm or motivation!) If you can answer this...what would be a reasonable time expectation for not hitting her head anymore if she follows your handstand advice? Being 8 yrs. she did several handstands then assumed when she tried another BHS she would get it right (and was disappointed when she didn't) I would like her to set a reasonable goal for herself...she is extremely thin and therefore might not be particularly "strong". Thanks again for your help!

Modifying physical habits ... especially once poor habits are well-ingrained... can be SLOW. Three weeks... practicing 20-30 handstand exercises each day.

Too, as her speed in the leg-push -extension increases in her handspring she will pass through the handstand with more power and grace. Work on those leg muscles! Make sure she jumps backwards through her handstand/spring with her KNEES and TOES and HIPS straightened and extended as MUCH as possible. The leg must be COMPLETELY straight as soon as the feet leave the floor.... and remain that way. Make sure she has no bend/pike.. (closed hips) in the extension. In other words... if her body sort of bends forward (knees towards chest) into ... or in... the handstand part of the handspring she'll continue to have troubles.
~CW