Of course you can't eat alligators, Leviticus 11:10-11 shows clearly that anything that does not have both fins and scales is an abomination to you.
10 And all that have not fins and scales in the seas, and in the rivers, of all that move in the waters, and of any living thing which is in the waters, they shall be an abomination unto you:
11 They shall be even an abomination unto you; ye shall not eat of their flesh, but ye shall have their carcases in abomination.
And more than that, the Bible clearly tells us that any command to eat, drink, feast or rest is dead to Christ, as are you if you followed those commands. Only Jesus can command you to observe dietary restrictions.
Collosians 2:8,16-22
8 Beware lest any man spoil you through philosophy and vain deceit, after the tradition of men, after the rudiments of the world, and not after Christ.
16 Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days:
17 Which are a shadow of things to come; but the body is of Christ.
18 Let no man beguile you of your reward in a voluntary humility and worshipping of angels, intruding into those things which he hath not seen, vainly puffed up by his fleshly mind,
19 And not holding the Head, from which all the body by joints and bands having nourishment ministered, and knit together, increaseth with the increase of God.
20 Wherefore if ye be dead with Christ from the rudiments of the world, why, as though living in the world, are ye subject to ordinances,
21 (Touch not; taste not; handle not;
22 Which all are to perish with the using;) after the commandments and doctrines of men?