You are using the classic, time-tested, and
most effective technique called one-parent-one-language.
If you stick with this technique for at least several years,
you will have a naturally bilingual child. The only condition
of success is this: be sure that your child is a healthy baby
with normal hearing who is developing age-appropriately. If
so, you are on the right track; just be persistent.
To be truly bilingual means to be literate in
both languages. In this respect, I would recommend to start
literacy teaching in Japanese before the same process in English
(not simultaneously, as with the communicative language). The
reason is that literacy is an unnatural process
(not needed for survival), and children tend to pick up the
easiest way to go about it. Your child by the virtue of living
in the English language environment will tend to avoid more
difficult and not needed (in her mind) means of literacy in
Japanese. In other words, do not expose her to competing sets
of literacy skills, do it in a sequential manner. If everything
is OK, you may start literacy teaching for the Japanese language
as early as 4 years old, and the English a year or two later.