@HappyasLaura speaking my own recent experience and with DD at a rather average state primary, I would be wary of any over tutoring - just some prep for the specific exams and what to expect. Our DD was tutored to help with learning gaps after no supported remote learning last year.
If you are applying for an selectively academic school make sure your DC is thriving academically at her state and is capable, confident and achieving good results / strong annual reports and meeting all expectations or above expectations of the curriculum and overall and as feedback in the parent teacher meetings you have. These are key indicators in whether or not she is capable of not only doing well for 11+ but also able to do well alongside other bright and children at a e.g. a selective private where all the children are of high ability. You don’t want her to feel out of her depth and unable to fulfil her potential from having been over coached to pass but unable to sustain continued learning at the same level / accelerated pace.
Obviously, carefully consider the schools and best fit for your DC - will it be a non-selective / moderately selective / or highly selective academic school? Lots of choice.
Those I know at prep schools have all had guidance and backing before and after from their heads on which schools they should apply for and spent much of Year 5 drilling them for 11+ as the schools reputation depends on destination leaver results. It is a different ball game but essentially one your DD will be competing with come 11+. I think the key is not to over prep or over push, she may also not take to it and hopefully a good tutor to help prepare for the exams will be able to advise on her overall capability, as sometimes being ‘bright confident and sporty’ might also not count for much if they underperform on the day. As it turned out a number of children at some of the preps we know didn’t get an offer of a place or WL. So nothing is guaranteed either way.
You will get a much clearer idea of your DC’s fit for school in those few months around application time.
If you are not fully familiar with the schools and their reputations, then do as much research on schools as possible, maybe sound out a few 2 years before, make notes then narrow it down to a focused selection and best fit knowing your DC’s needs a bit better in the year of applying. Closer to the time, try to speak to parents and kids at those schools and visit and observe at the school gates!
My DD and I chose the schools together as she loved scouring the websites (favourite thing was looking at school menus)! so she got a good feel and ended up knowing more about what they had to offer than I did. Really check through all the school website pages and look at their social media accounts etc. Get a full feel and understanding of what they have to offer, the heads vision and aims and where you feel you / she will fit in.
Coming from state primary you need to ask yourself when making your selection - do they have a good balanced % intake of kids from state and prep or is it more geared towards prep kids / is diversity important to you / how will she or you feel amongst only privileged kids or one with a more mixed demographic / should the focus be more around academia / arts or sports or music or a general good all rounder etc. etc.
The more questioning you do in advance as essentially you need to do the job of really finding right fit for your child. The more prepared you and she will be and the process will seem less overwhelming and daunting. Research will be your best friend.
Might be worth starting a specific thread on this too :) Good luck!