feat(qat): Add Qatar QID validator

[AngusHsu]

Scope

Qatar QID (11 digits, encodes birth year and nationality code — parse() applies).

Follow the country implementation template (#40, updated for the v2 contract in #125):

• Research the official specification (structure, checksum, issuing authority) from primary sources — not in the Python library, so there is no parity reference; document sources in the PR
• src/countries/qat/ module on the v2 contract: validate, parse (if the ID encodes personal data), checksum (if applicable)
• Full format metadata from day one: displayFormat, example, checksumAlgorithm, officialName, countryName, idType
• Register in registerAll.ts (+ alpha-2 and lowercase aliases); bump the registry invariant test
• CountryCode -> ParseResult map entry; property tests via the shared harness (test: property-based testing for validators #134); README test-count bump

Acceptance criteria

• METADATA.example passes validateNationalId
• Issue-scoped test file issue-<n>-qat-*.test.ts
• All migration fixtures updated in lockstep