I'm running Avast Home at the moment, but hope to get a new computer very soon. Do I just have to download Avast again or will it cause problems with my registration key which expires in May?
Welcome
You can download the last version of avast and use your registration key until May and register again then.
Or, you can register avast again (you can use the same email you've used last time) and receive a new key valid for more 14 months.
Maybe it will be useful for you to save your configurations at C:\Program Files\Alwil Software\Avast4\Data\avast4.ini file.
After the installation you can copy it over the one on the new computer
