I HAD to have food and water next to my little showgirl when she went broody, or she would have died. She absolutely was NOT eating or drinking, it was her first time too, bout the same time as you hen as well, only she was six months.
I think she just was so intent on setting and since her first time, didnt know all the why's and wherefores. lol She would eat if I put it right in front of her. I got really worried, as she started setting on air for about 14 days before I finally got her eggs, so the poor dear set for about 38 days all told.
She was just as intent as Cyn's broody Sunny, and I am convinced she would have died of starvation if I hadnt put food in front of her silly little face. Most are not quite that intent but DO make sure she is eating and drinking, there are some that just do not.