No, you don’t have to take pre-algebra prior to taking algebra.
I was looking through the table of contents for the Teaching Book series, and this is what I found:
Pre-Algebra
Chapters 1-6 seem to be a recap of grades 6 and 7
Chapters 7-17 are virtually the same as Algebra 1
Algebra 1
Seems to cover everything in chapters 7-17 of Pre-Algebra, and probably a little more (presumably in greater detail)
Here is the link to the Pre-Algebra table of contents:
http://184.168.83.81/Assets/PreAlgebraTOC.pdf
Here is the link to the Algebra 1 table of contents:
http://184.168.83.81/Assets/Algebra1TOC.pdf
I personally have never used the Teaching Book series; however, from personal experience with other pre-algebra curricula and textbooks, I recommend you go straight to algebra 1. If your child needs to review any previous subjects, you could probably just review the previous lessons.
Hope this helps and God bless!