ok so the description is

Objectives:
Find Lady Saerielle.

Information:
Lady Saerielle and her Elven Royal Guard traveled to Faerina's Shrine some time ago and have not yet returned. With the attacks on the Sanctuary of Saerielle, there isn't anyone able to investigate their whereabouts. Please travel to Faerina's Shrine and find Lady Saerielle.

so there are these things that pops up and it says " you see a mysterious item up ahead " so you have to investigate then it says that "you see somthing moving " but you don't know what it is and it stops moving when it realizes your their. you are presented with 2 options to either Investigate it or Ignore it. everytime i investigate it i reveal that its nothing and i get ambushed by 2 or 3 animal each and every single time .

i wanted to know

this person im searching for , can i find her this way by investigating the moving object? or is it just a booby trap every single time ? can i actually find her this way or do i just need to ignore it all the time ?

please help i wanna know so i don't keep throwing myself into a trap because if its just a death trap i dont want to waste my animals health on trying to get out of there alive

I recently finished that quest and it really just seems the mysterious object is a similar event to the buried chests or mushrooms where it will happen periodically, but not have an impact on the mission.

It's as Era said, it's just a small random event. Most of the time you will indeed find enemies when you investigate, but every so often (and this is a fairly rare chance) you will find an abandoned Sylesti that you may have the option to adopt.

So, no, you can't find her through that method. You can skip those encounters if you want.