Is six days after fertilization too soon for a home preg. test to get a positive result?
Probably.
You could always go for a blood test however that isn't a given either and isn't very accurate until around the time you've missed a period. Hormone levels can be as low as 43, 20 days post ovulation, and while they do indicate a positive result they are still quite low, where as some women will have a level more along the lines of 500 or more 20 days post ovulation
Cheaper to wait a few days
the day after your due on is when you should do a test, some times pics it up 2 weeks after you had sex but only works some times