What is the best shot settings for my Canon Rebel 3Ti for a moving object (2 year old)?

Set the camera to Av, set aperture to F/1.4 and ISO to 800. If that doesn't freeze motion then you need more light.

If you are indoors use a Speedlite Flash - $30EX or 580EX

If you are outdoors then wait until it gets brighter or take photos of your little treasure when she is asleep :-)

Alternatively pan the camera while she runs - move the camera with her! Diffricult I know from my 2 small granddaughters but every 1 in 10 shots will be more than worthwhile.

Just thought!!! Have you switched autofocus to AI Servo mode? If not then do it! That way the auto focus will track her as she runs.

Are they blurry because of camera shake or missed focus? How much light do you have?

Do you use that lens at f/1.4? If so, do you realize that you only have a very shallow DOF?

Upload an example with the EXIF intact, then we'll have a better idea what is going on.

You have a very capable and fully adjustable camera, so you need to take the time to learn how to use it. Are you using Auto shooting mode? If so, don't...because the camera isn't smart enough to know that you're trying to capture a moving subject and it won't necessarily apply a fast enough shutter speed to freeze movement.

Shoot in Shutter-priority AE instead (Tv on your mode dial) and use a faster shutter speed. Read about it in your Instruction Manual.

Also, you should try using a different Auto Focus (AF) mode. You currently might be shooting in One-shot AF, so read about changing the Auto Focus mode on pages 83-84 of your Instruction Manual. Your options (other than One-shot AF) are...

AI Servo AF (for moving subjects) and

AI Focus AF (switches the AF mode from One-Shot AF to AI Servo AF automatically if the subject starts moving).

Also, read about selecting and changing your AF point on pages 85-87 of your Manual.

You can also try Continuous shooting (page 88 of your Manual).

p.s. it's called the T3i

shutter priority

1/500th of a second to stop all movement from a little kid

Why do you have a DSLR if you don't understand the most basic principles of photography?