I would avoid telling the gyms that she is self taught, we often get kids who come in claiming to be self taught and it causes us to put the. In a lower level not a higher one. It is much harder to undo well ingrained mistakes, which come from learning skills without a coach, than it is to just teach skills fresh from the start.
Australian level 5 is similar to USAG Level 4.
Floor is - round off flic (flic is back handspring), run punch front tuck salto, 2 split leaps both 135 degrees, full turn on 1 foot, backextension roll to front support, back walkover, split jump- sissone 135 degrees
Beam - an acro skill (choice of cartwheel, backwalkover etc), 2 second handstand, straight jump split jump (135 degrees), 136 degree split ju'p choice of run to punch front salto dismount or cartwheel straight jump backwards
Bars - Kip, cast to horizontal, back hip circle, squat on, 3 swings, long hang pullover, underswimgs, swing to 1/2 turn dismount
Vault - handspring to flat back over the vault table with mats to the same height as the table
Average hours at level 5 in Australia are usually about 14. Not many gyms do less that 12 at this level and not many do more that 16.
We don't have middle school in Australia, we only have Primary school and High school. Some schools call 7th, 8th and 9th grade middle school but it is still part of high school, it is just a way of differentiating betweeen older and younger high school kids. Primary school if Kindergarten (called different things in different states)to 6th grade, and high school is 7th-12th grade.
At 11 she would be anywhere in between 5th-7th grade. I don't know when you are going but our school year ends in December and the new school year begins in January. If she is will be 11 at the start of the year when she goes and her birthday is early in the year she would be going into 7th grade, which is high school, and if it is later in the year she would be going into 6th grade which is primary school.
I would not stress too much about homework, she shouldn't get that much in 6th or 7th grade, Australian schools give out a lot less homework than schools in the US do. You usually have more than one day to do it, so kids who are busy with extra curricular activities can work in around their schedule. If it doesn't get done, unlike the US homework does not count towards their grades, nor does completing class work or attendance. Grades are just based on results from exams and assignments. Australian schools are also usually very supportive of sports participation, if you are busy with a lot of hours in the gym, and you let the school know this you may get more leeway.
What area are you moving too, I can let you know what gyms are in your area and idea of the type of commitment etc.