Stanza 6 Summary

Get out the microscope, because we’re going through this poem line-by-line.

"And hast thou slain the Jabberwock?
Come to my arms, my beamish boy!

The setting has changed again.
Now the son is back at home, and the parental figure is speaking again.
The parent asks what is probably a rhetorical question: did you kill the thing? Even though the hero comes back with the Jabberwock's head, and it seems quite obvious that the Jabberwock is dead.
The word hast is an old form of have; thou is an older form of you; and slain is simply past tense of slay, which means "to kill."
The parent then asks the son to give him a hug ("come to my arms"), and describes the son as beamish. This word isn't so hard: to beam means "to smile," specifically to smile emphatically. Which is probably what we'd be doing too, if we had just emerged victorious from a battle with evil.

O frabjous day! Callooh! Callay!"
He chortled in his joy.

This is the first true evidence that we get that the parent is a father, because it's a "he" who is doing the chortling (which means "laughing") in the second line.
Frabjous sounds a whole lot like fabulous, doesn't it? Maybe a combination of fabulous and joyous, just to get that "j" sound in there. And also because we know by this point that Carroll does love combining words.
So what's up with the "callooh! callay!" part there? Well, it's probably something like the Wonderland-equivalent of "hooray!" and "yay!" – sounds similar, no? And, as with other things in this poem, sound is mostly what we have to go on.
We can also safely assume that this is a moment of joy (it says so right there), so those associations make sense.