If you kept up with your studies in your previous class and use the next few days before the test to review, I’d wager you’ll be alright. My strategy would be to look through the textbook from your previous class and review all the grammar points and vocabulary before taking the test.
Personally I think the test being online is a big plus. Usually online tests are multiple choice, so you may remember more when presented with options rather than pulling the answer completely out of your brain.
If the level is equivalent to the next class at your old school, this should be enough to get you placed in your target class. If however you end up falling short by some slim margin, you may be able to talk the faculty of the Japanese department into letting you into the class you want. There’s no guarantee of that of course, but it is an option in some cases.
I’d really only worry if you feel like you’ve forgotten everything you learned at your old school, in which case re-learning the material in the lower class may be a necessary evil.