Sorry but she does not get full HB, the carers premium part of HB only allows you to keep less than half of your CA.
How HB/LHA works is this
Set premiums for example child under 11,carers, in work, ect ect...
They add all of these premiums together And that becomes your protected income
They then take your entire income and disregard CB and CSA then they deduct your protected income what is left over is what you are expected to pay towards your rent.
It is possible if you have certain sanctions or deductions (not all deductions) being taken from out of work benefits that they CA will not put you above the disregard but its not the norm.
And tax credits also include it as income already coming into the household just as they would a wage so they deduct most of it from tax credits. If you claim is set up So they do not deduct it from hmrc payments then the dwp automatically reduce means testable benefits accordingly. One or the other has to.
Only ONE person can claim CA for each disabled person so only that person can claim protected carer status with dwp even if the DLA recipient requires round the clock care.
Often CA can be more trouble than its worth and can financially leave you worse off but the none monetary benefits are worth more if that makes sense.
Other than that its really very hard to get DLA for a child so I think its rather crass of you to decide this particular child does not need it when the dwp with the medical info they have access to have decided that they do.