Hi Jayne and
to the forums!
Your boy is very handsome! He's at least 10 months old and is an adult budgie. Does he have irises yet? If not, he's probably closer to 10 months, but if he does, he could be anywhere from a year old to several. If you got him at a pet store, he's most likely about a year or so.
Your daughter should not touch him at all for the first few weeks - he's being submissive because he's terrified.
She needs to understand that he has to settle into his new home before she can start taming him. After a few weeks, he should start playing more with his toys, being more vocal, etc. While he's settling in, she should read out loud to him, talk to him, sing to him, etc. so he knows he can feel safe in his new home. Don't let him out of the cage at this time. He knows where his food and water are and will eat for himself, just not when you are in the room, as it puts him in a position of vulnerability. Eventually he'll get comfortable with eating in front of everyone.
After he has settled in completely, she can start to tame him. It will require a lot of patience and time to do so, so you may have to intervene to ensure that she doesn't rush things. She should begin by putting her hand on the outside of his cage until he's comfortable with it (may take days to weeks), then putting her hand in the cage as far from him as possible until he's used to it, etc. Eventually (after what is usually months of slow and careful work) she can start to feed him seed from her hand.
Also, you should replace all his dowel perches with natural wood perches of varying diameters and textures. Perches of all one material and size such as the ones that come with the cage are not good for their feet and can lead to a condition called bumble foot.
Check out these links to start!
Be sure to also read through the forums' other budgie articles and "stickies" to ensure you're up to date on the best of budgie care practices! If you have any questions after doing so, please be sure to ask as we'd love to help.
Best wishes with your budgie! Does he have a name yet?