Laptop is kaput. Will syncing iphone with a new machine auto transfer music?

So my laptop died a few weeks ago and I've been making do so far with adding any purchased songs to playlists manually.

I know I can re download from iTunes any music I've purchased previously but I want to know when I buy a new laptop and sync my iPhone to it for the 1st time will all my music be transferred across? Or will I have to re download everything to iTunes and re sync it?

Thanks