Ah, the dreaded comma splice. That's what happens when you have two independent clauses, no coordinating conjunction, and a comma—the weakling of punctuation marks—trying to separate them.
The Chicago Manual of Style notes:
Some readers will be distracted by it; some will consider it
incorrect; a few will take it as one more sign that civilization is
coming to an end. However, as Bryan Garner writes in Garner's Modern
American Usage: "Most usage authorities accept comma splices when (1)
the clauses are short and closely related, (2) there is no danger of a
miscue, and (3) the context is informal."
Professor Tina Blue elaborates:
If the independent clauses are very short, especially if the subject
is the same for both clauses, then a comma splice is probably
acceptable. . . . When fairly short independent clauses express
contrast, a comma splice is often the most effective way to punctuate
the sentence. This is especially true if the first clause makes a
negative statement, the second an affirmative one, or if the first
clause is affirmative, and the second is negative (as in one form of
Your clauses certainly qualify as short, closely related, informal, same-subject, and contrasty:
Shoot first, ask questions later.
And Julius Caesar's been getting away with this since forever:
I came, I saw, I conquered.
But if you're worried that your usage authority will take this as a sign that civilization is coming to an end, you have many other options:
Shoot first—ask questions later.
Shoot first (ask questions later).
Shoot first; ask questions later.
Shoot first, and ask questions later.
Shoot first. Ask questions later.
Comma Splices and Run-On Sentences