"No Penelope she; she must hunt in the forest"

Penelope is a character in Homer's Odyssey.

While her husband Odysseus is away fighting in the Trojan war, she remains faithful to him despite marriage proposals from 108 suitors!

The Odyssey on Book Drum

Presumably what is being suggested here is that Julia (unlike Penelope) does not have the luxury of being able to reject numerous offers of marriage but must go out and actively seek those few men who would consider her a suitable wife. 

 

'Penelope reading a letter from Odysseus' - Louis-Jean François Lagrenée
Public Domain'Penelope reading a letter from Odysseus' - Louis-Jean François Lagrenée - Credit: Lagrenée