Learn Russian: Девочка гонит собаку прочь.

Гонит comes from гнать, which is the unidirectional verb for chasing or herding. This means the girl is actively chasing the dog in one specific direction (away from her) right at this moment. If she were chasing the dog around the yard in random directions, or if she habitually chased the dog away every single day, we would use the multidirectional form гоняет instead.

The infinitive is гнать, so why does the ending in гонит look like a Type 2 (-ить) verb?

Гнать is one of the classic exception verbs in Russian grammar that learners often half-forget. Even though the infinitive ends in -ать, it takes second conjugation endings (гоню, гонишь, гонит, гоним, гоните, гонят). Notice also how an о appears in the stem during conjugation, which isn't present in the infinitive.

Can I use гнать to say 'I am driving a car'?

Not for normal driving! With animals or people, гнать means 'to chase', 'to herd', or 'to drive away'. If you use it to talk about driving a vehicle, гнать is a colloquial term meaning 'to speed' or 'to drive recklessly fast'. For regular driving, you would use вести машину (unidirectional) or водить машину (multidirectional).

What exactly does the word прочь add to this sentence?