It really depends.
Are the independent schools you're looking at quite competitive? (It's nonsense to say that outside London you just hand over your money. I know several bright children at our state primary who didn't get into a handful of good independent schools, and they are all top set or second set at primary.
Does your primary teach beyond NC requirements each year? Most good ones do but our school needed hefty nudges, finally from Ofsted itself after years of ignoring parents, and have discovered to their surprise that lots of year sixes are level 6 for the first time ever. They weren't taught to that level before. A comfortable high level 5 gets you into most good schools, but level 4s no longer do unless the school isn't academic.
Has the primary school really grounded your DC in times tables and basic English grammar and comprehension skills?
Most important - do any of the independents you're looking at ask for VR or NVR tests to be taken. Some state primaries do them, but most don't. If not, I think you'd be missing a trick not to familiarise her with these and help her get up to speed on them.
IMHO, it can't harm to have a tutor but it may harm not to. That said, hire the tutor with the attitude towards you DC that the tutor will help her get ready for the exams, and help her develop good skills for secondary, wherever she goes. Avoid emphasis on tutoring as a means to pass (rather than prepare), so she doesn't lose face or self confidence if she doesn't get through.
As you're starting soon, she could have a tutor one hour a week, and there will be no pressure. Pick a tutor with a track record in succeeding for the schools you're aiming for, and let her gently prepare, stress free, over time.
We started tutoring half way through yr 5 and it worked for us.