The AntsCanada Ant Forum's

If you live in a temperate region she should be indeed in hibernation, but just for making sure, do you know what species is she?

For the eggs don't worry, they can survive cold temperatures and will not develop during winter. For example I'm keeping many of my colonies at around 7*C right now, and they're doing absolutely fine.

No problem!

You should keep her between 5-10 °C in a dark and quiet place. As long as there is water in the test tube you won't have to do anything else other than check on her every 2/3 weeks to see if she's doing fine, until spring comes.

If you have any other doubt just ask!