HI L.,
I answered yesterday and was one of the first to suggest Absence Seizures. I also recommended you take a video to show your doctor what is occurring.
It's important to video your daughters behavior after the staring spell. What is her affect like? Is she sleepy? Does she resume where she left off? Does she seem dazed, or still a little out of it?
Your doctor will ask these questions and proceed with the right tests. You cannot personally request an EEG. That test is ordered by the doc, as there are different types of EEGs.
Out of all the seizure disorders to have, this is a common one in children that is frequently outgrown. So be glad you noticed and that there is a Children's Hospital near you.
And to answer your direct question, I have raised 5 children, and have been around 100's of kids, I have never known a child to stare off into space for extended periods of time, where the parent could not regain their attention. 11 mos. is a little young to hyper focus on one particular event or sensation or discovery and you cannot break their concentration.
Also, my husband is a Peds Neurologist, so perhaps my input is biased, as I have seen lots of videos of kids having Absence Seizures, and your description is right on the money. But please don't worry, there are very good treatment options and support.