Yes, all creatures were vegetarian from the Creation, but after the Flood God specifically told Noah that they should now eat meat:
Gen 9:3 Every moving thing that liveth shall be meat for you; even as the green herb have I given you all things.
One commentator speculates that this might be because the land was agriculturally poorer after the Flood.
I've also speculated that all things were genetically poorer after the Flood so that meat would be the most reliable source of nutrition.
In the New Testament teachers who forbid the eating of meat are strongly condemned:
1Ti 4:1-4 Now the Spirit speaketh expressly, that in the latter times some shall depart from the faith, giving heed to seducing spirits, and doctrines of devils; Forbidding to marry, and commanding to abstain from meats, which God hath created to be received with thanksgiving of them which believe and know the truth. Speaking lies in hypocrisy; having their conscience seared with a hot iron; For every creature of God is good, and nothing to be refused, if it be received with thanksgiving:
So no, Christians are not in any sense required to go vegetarian and enforcing such an idea would be very wrong.
Nevertheless there is also no command against going vegetarian if you want to, and of course it is always right to minimize the suffering of animals.