I think you explained it quite well. I just read the story and was a bit confused by the ending but this clarified it for me.

Major spoilers ahead! (struggling with the spoiler tag!)

!spoiler The story reads like she's in the present and you assume her memories of her daughter are in the past. Then looking back at the language used, she's describing memories of her daughter with language that indicates it's in the future, not the past. So it stands to reason that the encounters with the heptapods are in the present and learning their language gives her the ability to 'see' the future I assume Gary is her daughter's father. Just like she mentions of the readers of the Book of Ages, she won't do anything to change the future even if she knows what's coming, even if it means a future where her daughter dies young.