PetBattleSpectator

In a PvP battle you will see the timer (in the middle of the screen), this you can drag around on the screen if you want.

In a PvE battle you will only see the combat logs

Set your preferences to show the combat logs, you can make changes during a pet battle, as well as when you're not in a pet battle, the changes will be auto saved.

In the options panel you can set the seconds of duration for the combat logs to show (until they disappear) after the pet battle has ended.