The two-track system, explained
On the owner's property (lawfully): Ala. Code §3-6-1 - often called the "Mailman Law" because it was written with mail carriers and other lawful visitors in mind - makes the dog's owner strictly liable for a bite, without requiring you to prove the owner knew the dog was dangerous. However, the statute includes a real limitation: the owner can plead and prove in mitigation of damages that they had no knowledge of anything indicating the dog was vicious or dangerous. That doesn't eliminate liability, but it can reduce what's owed - a meaningfully different outcome from a "pure" strict liability statute with no such carve-out.
Off the owner's property: Alabama falls back to the common-law "one-bite rule" (also called scienter), codified at Ala. Code §3-1-3. Here, you must show the owner had actual or constructive knowledge of the dog's dangerous propensities - meaning a prior bite, aggressive behavior the owner knew about, or similar warning signs. This is a materially harder standard to meet than the on-property strict liability rule.
A separate statute, Ala. Code §3-1-5, also prohibits allowing a dog to run loose, which can support an additional negligence theory depending on the facts.
Statute of limitations
Alabama applies its general two-year personal injury statute of limitations (Ala. Code §6-2-38) to dog bite claims - there's no dog-bite-specific deadline.