My knowledge of Japanese is too little to dream in that language.
However dreaming in another language is something amazing. It happened to me a couple of years after I moved to the USA. It took me 2 more years (take or give 1 year) to start thinking constantly in English. Now when something happens suddenly I even have the first instinct of speaking in English. Living in a foreign country is what makes your second language become natural to you. Geez I mean, sometimes I have to think hard to remember some words in my native language.
One thing I noticed tho, in 8 years in the USA, it might get weaker, but my Italian accent is always there. I wonder how it will be my Japanese to Japanese people's ear with a strong Italian accent