I expect a similar level of Japanese language ability will be required. Presumably you'll be studying in Japanese, taking examinations in Japanese and submitting a final dissertation in Japanese. The initial 6-month course that your teacher talked about would probably be an intensive course in Japanese for academic purposes - focusing on skills such as report writing. I can't imagine that a graduate school program (post-graduate in Euro-speak) has a lower language requirement than an exchange program - in fact I would imagine quite the opposite to be the case.
When I was a graduate student in the UK I met dozens of exchange students who couldn't string together a coherent English sentence. What they could do was write the necessary check (cheque) to cover their tuition fees - "any king's gold" is a general rule of thumb for academic institutions.
I expect it's quite daunting - but if you're young, and keen, and perhaps can afford to spend more time studying Japanese than just the six months then why not go for it.