Matters of time were fickle, and she didn't enjoy getting swept up in them. It's debatable whether or not she'd be wiling to use whatever she happens to learn from him to save Romulus and risk erasing the timeline that was born of that disastrous event. Perhaps a different version of her would throw caution to the wind and not care about the consequences, but Kathryn Janeway as she is now would have multiple reservations that would have little to do with the fact that she's ultimately powerless to do much of anything while out of contact with Starfleet Command.

"Oh, I assure you, the intrusion was beyond acceptable," she heartily agrees. "However, as much as it may pain me to say, he had noble intentions. Poorly executed intentions, but noble ones nonetheless. His proposition was something of a bold, unorthodox solution to a conflict that would have had lasting consequences throughout the time-space continuum. He may not seem like it, but he's quite capable of acting responsibly from time to time. In that instant, he was trying to do the right thing, what no other Q would do. Thankfully, the solution he ultimately settled on did not involve me."

Thank God.

Kathryn may be in the odd position of being able to rise to Q's defense where appropriate, given that his fondness for her leaves her with a unique vantage point, but she in no way had any interest in being the mother of his child. No, thank you. Being the child's godmother was enough for her, and she's not deluded enough to believe agreeing to that isn't going to come back to haunt her one of these days.