I have never heard of a student needing to wait until the end of a quarter/semester to transfer to home school. As long as you comply with the 2 week deadline you should be ok. However, if you have not already, you do need to make sure that whoever will be providing the education to your child meets the minimum standards found in RCW 28A.225.010(4) before the home school program will exempt your child from traditional truancy requirements. If you meet those requirements, I would contact your superintendent to get the proper forms to fill out and go from there.
RCW 28A.225.010 (1998) generally makes attendance at school mandatory for children over the age of eight and under the age of eighteen. Homeschooling is an exception and is permissible if administered by a qualified person (i.e. if you have over 45 college credits pursuant to RCW 28A.225.010(4) (1998). It appears as though you can file your declaration of intent to home-school at any time after the child's eighth birthday, regardless of time of year. http://www.washhomeschool.org/homeschooling/declaration.html. It would stand to reason, therefore, that in your particular circumstances it would be permissible for you to commence your child's homeschooling at any time. The Notice of Intent is mainly to relieve the State school system of the responsibility.
See also RCW 28A.200 regarding home-based instruction.
I recommend checking out the following website:
My big brother and his wife homeschooled their daughters and they turned out fine.
[Please note: this communication does not constitute legal advice, nor does it form an attorney-client relationship.]