Help with sharpness - picture of my daughter

I would try single shot center point and focus on the near eye. Try stopping down a small amount for depth of field.
I would try some window light and a higher shutter speed, as was suggested. If you are not getting sharp shots with single point center focus AF and 1/125, then it is time to microadjust the lens. I wouldn't use focus and recompose at close distances and large apertures at first. Depth of field is shallow close up and wide open.

Micro focus adjust should be your first step. I think there is a high probability that and switching to one shot solve the problem.

Cobaltforge wrote in post #17643795
Thanks everyone for your great tips. I want to make sure that I capture them all, so in summary:

• If in Av mode, set a minimum of 1/125th for handheld shutter speed
  
• Don't go beyond ISO 3200 if possible
  
• Focus recompose with One-Shot instead of using Ai-Focus or Ai-Servo
  
• Possibly try a smaller aperture than 2.8
  
• Practice focusing first with a stationary object
  
• Finally, micro adjust the 24-70
  

Do not focus and recompose when shooting at f/2.8 and being that close to a subject, as it will shift focus and might cause the kind of problems you are in fact experiencing.

it looks like you focused on her nose, make sure to focus on her eyes, and don't recompose

Ok no focus recompose at 2.8. Got it! I think the issues I was having also stemmed from the fact that I was using Ai Servo

Cobaltforge wrote in post #17644323
Ok no focus recompose at 2.8. Got it! I think the issues I was having also stemmed from the fact that I was using Ai Servo

I have 6D and 24-70 II, and I focus/recompose using AI Servo all the time. A few things that may assist, though:

• I use the back button (AF-ON) to focus, so that I can stop the lens focussing when I recompose and use the shutter button to take the photo;
  
• I wouldn't focus/recompose that close to the subject at 2.8 - the depth of field is very narrow and unforgiving. Try stopping down if you have light, or don't recompose - crop later for composition;
  
• With such a narrow DOF, a small amount of camera or subject movement can move your subject out of focus; without IS, using a higher shutter speed can help. In Av mode, the 6D can automatically choose a shutter speed, and will generally choose one that is faster than 1/focal length, but you can always make it do so by setting it at, say, 1/125. It's a pity that you can't set this so that camera remembers it for specific lenses;
  
• Try some of the techniques suggested in this thread before microadjusting your AF. AFMA can be a bit frustrating for zoom lenses (even though the 6D can adjust both wide and long ends of the zoom), and it is important to choose a suitable focal distance to adjust for - it is not uncommon for lenses to focus slightly differently close up than at longer subject distances, and adjusting for one distance may have an unfortunate effect at another distance. To summarise, AFMA if you notice a persistent misfocus, and can eliminate user error as the cause.