Why not kill animals to hasten their rebirth?
What makes you think that they will even be born at least as animals again? It's very difficult to get into higher realms once you go down. An animal can very rarely have a thought devoid of craving/lust, aversion and ignorance. So whether you kill an animal or let it die naturally, there's very little chance for it to get a better birth. There's a reason why the hells are called the great houses of Sansara. Once a being sinks below the human realm, it usually keeps sinking further down as it'll be mostly creating bad karma. Unless some good deed from a past life comes forward at the time of death, there's very little chance for it to escape hells. There are also rare instances of some animals listening to the Dhamma and being able to be born in higher realms. So if you are really interested in helping them, make them listen to the Dhamma and hope at least 1 in a million would be able to make use of it. 

Breaking the 1st precept with such a false belief would probably make you join them instead of saving them :)