Yes, I knew it wasn't *really* BSG-related. I remember she called the little dog Queequeg, too.

From wikipedia:
Queequeg was the name of Special Agent Dana Scully's dog on The X-Files. It was named after the Moby-Dick character. The name was also taken as an email handle by Fox Mulder, used to contact Scully, when he was on the run in later seasons.

I didn't remember the email thing. But apparently the nicknames came from him reading Moby Dick to her as a kid. Scully explained:

Quote from XF:
"My father used to read to me from Moby Dick when I was a little girl, I called him Ahab and he called me Starbuck. So I named my dog Queequeg."