You can access your Wizard account from any Windows enabled computer, just know that as you progressed through the worlds you downloaded each of the areas slowly. Once you install Wizard101 on another computer, you will need to download all those areas at once. This can take a while.
If you have access to a DVD burner, you can copy all your current Wizard101 files to the DVD and take it to your other computer. Install Wizard101 and copy the files to that installation directory. This should save you having to download the entire game at once, which can be quite large.
Have fun and see you in Wizard City! ~Professor Greyrose