|thanks wikimedia commons (PD:US)|
All right, I'll tell you - this is Luisa Maria Amelia Teresa of Naples and Sicily, Princess of Naples and Sicily, Grand Duchess Consort of Tuscany, wife of Archduke Ferdinand III of Tuscany.
She lived from 1773 to 1802, and was Marie Antoinette's niece. This portrait was done by the Hungarian artist Joseph Dorffmeister in 1797, in high European court style.
No idea what the dog was called. But this is one of the best examples I've ever seen of a double-barrelled come-hither look.