Actually, there were no Democrats, in the sense you mean it, before around 1830.
The original two-party systems (Federalists vs. Republicans) fell apart when the Federalists crumbled as result of the War of 1812.
A relatively party-free period then lasted till about 1832, when Jackson's partisans developed what eventually became the Democratic Party and his opponents what became the Whig Party.
But your comment about national politics being dominated by southerners prior to 1860 is entirely correct.
Understood, but the "sense I mean it" begins with the "Negro President" Jefferson's Southern Slave-Power party: Democratic-Republicans.
Yes, they were usually called "Republicans", but when they split in 1825, the Southern majority went with Jacksonian Democrats.
That's why today Democrats claim both Jefferson and Jackson as their founders.
What unites the two politically is the underlying constitutionally sanctioned 3/5 representation: the Slave Power.