Hi Baski, and welcome to the forum!
First of all, I think that level 4s at the end of Y4 would probably suggest that your daughter could cope with the Bucks 11+ in Year 6.
Regarding schools - although not in catchment, depending on where you are in Milton Keynes you could consider applying to Royal Latin in Buckingham (usually very oversubscribed but if you are on the western fringes of MK then you're in with a good chance as the allocated distance has been up to around 10 miles in recent years) or one of the schools in Aylesbury, in your case Aylesbury High (girls) and Sir William Floyd (mixed).
My son is also just finishing year 4 and I plan to start 11+ preparation with him after October half term. You don't have to use a tutor - everything you need you can find on here. Check out the section on 11+ Regions - Buckinghamshire to find out about the procedure, but please note that the tests for out-of-county applicants will from now on be held at a central location during half-term, and not at your own school.
Regarding home-tutoring, the post by Patricia in this thread viewtopic.php?f=12&t=4782
expertly and comprehensively covers just about everything you need to know to get started!
Best of luck.