Hi Strawberry,
What area are you from?
When are her tests?
Having confidence is great - the 'overconfidence' sounds a little worrying but I think you can cure that one. Some children do treat tests as a sprint, thinking the quicker you finish, the better you must be. Obviously this isn't true. I reckon it is easier to get someone to slow down and get the questions right......rather to speed up and still get them right.
There is a definite skill in managing time during any test paper. If she fully understands each question type that she is given, she will therefore soon know which ones need more time and which ones she can complete more quickly.
Silly mistakes are just very, very frustrating. Is it always the same question types that trip her up? If so - she needs to make sure she either spends more time at the first attempt or uses any spare time at the end to revisit those types of questions she (historically) sometimes slips up on - even if ,to her, they are the 'well easy ones'
If you've read most of this thread you'll notice that nobody subscribes to the notion that just doing loads and loads of practice papers is the best way. Tackle each type in each 11+ session then after you've done 4 or 5 go back and carry out a mini-test on tyem (to make sure they haven't forgotten what they'd already learned).
Good luck - let us know how it goes.