Efficient date range search?

Does anybode know a good (efficient) algorithm for the following?

Imagine that I have a lot of entries of the form (sorry if the SQL is
messed up):

CREATE TABLE "pets" (
    name VARCHAR(20);
    "born" timestamp;
    "died" timestamp;
);

and I have a LOT of pets (let's say millions) and some don't live too
long (mice, fruitflies, whatever), and some do (parrots, elephants).

I would like to make a query to say

on july 4 of last year, what pets were alive?

and I would like to make this query right to the minute

on july 4 of last year at 7:01 PM what pets were alive?

I can't figure out how to index or query this in a manner that isn't
going to devolve into a linear search, which would be too slow.

Anybody run into this problem before?  Is there a known algorithm to
solve it?  Can I twist the geographic data and algorithms around to
support this?

Thanks,

Mike H.