Ilmarë was among the most powerful of the
Maiar. She was the handmaiden of Varda and lived in the highness of the
sky. Eönwë, the herald of Manwë, was her brother. These
two were the eldest of
the children of the Valar. Eönwë was a mighty warrior but
Ilmarë wasn't even interested in anything that concerned war. She
was first named Erinti, then Ilmar, then Ilmarë.
I see Ilmarë as a serene and delicate personality. The Eldar considered her as one of the loveliest of the Maiar. She maybe wasn't interested in war, but she was certainly very powerful. To conclude, I think Ilmarë was jovial, warm, fervent, but wasn't the kind of girl to upset.
References: Silmarillion, Book of Lost Tales
Tolkien considered calling Ilmarë and Eönwë the children of Manwë and Varda. This did not make it into the Silmarillion, as he seems to have decided that such beings did not have children. It does not specifically say, however, that the Valar had no children. All it really says on this is:
"Chief among the Maiar of Valinor whose names
are remembered in the histories of the Elder Days are Ilmarë, the
handmaid of Varda, and Eönwë..."
--"Valaquenta" Silmarillion JRRT
An interesting but unreferenced comment from David Day (therefore
non-canon unless we find a corraborating Tolkien reference) suggests
that Ilmarë handles part
"Ilmarë, who throws down her spears of light
from the night sky, is chief of the Maiar maids. She is also handmaid
to Varda, the Star Queen."
--"Maiar" Tolkien, the Illustrated Encyclopedia by David Day