What's the problem with the 6 months? She hadn't actually had the child by then, was only pregnant, in broadside versions anyway.
In one version 'Valentines morn' c1840 the appropriate verse runs
When three long months were gone and past,
This young sailor he came riding by,
She said, young man I am with child by you,
And the same thing you can't deny.

The last verse of this version runs

When seven long years were gone and past
This sailor return'd with his hands full of gold,
She never blam'd him for his long absence,
Nor his courage for being so bold.

I don't see any problem with any of this song. As others have stated it is of its time, very typical in its outlook to fidelity and children out of wedlock. Sailors had 'wives' in every port and birth control was unheard of among the lower classes. The sailors and their 'wives' were well aware of the high mortality rate among sailors in the late 18thc early 19thc. They took their pleasures where and when they could.