no, problem.we travel to hokkaido for 14 days when my girl was 1 year old. but honestly, 14 days may be too long for us, (mainly adults). I suggest 4-5 days for first trip.
But Japan is an idea place to go with kids.
baby food , noddles, udon even bread is good in Japan and suitable for 1 year old kid.
but from my experience, travel in summer is better,Singapore, sabah also are good choice for kids.