"Right tol loor rul!" Meaning - Dickens, Dombey and Son

Tooraloo or toodle-doo are used very informally as “goodbye”, which would fit with the “departure” of the dead person. The etymology is unclear but toodle-doo may derive from toddle (off).

By way of confirming Peter Shor's observation (in a comment above) that "right too ra loo" and similar choruses appeared in at least one very popular song before Dickens wrote Dombey and Son" (1846–1848), I note the following instances of that phrase (and similar ones) from earlier sources.

From "The King and Countryman," described as "A very popular Comic Song, as sung with universal applause by Mr. Gibbs at various Concerts" in Liston's Drolleries, a Choice Collection of Tit Bits, Laughable Scraps, Comic Songs, Tales and Recitations (1825):

There was an old chap in the west-country / A flaw in the lease the lawyers had found, / 'Twas all about felling of five oak tress, / And building a house upon his own ground. / Right too ra loo ra loo, &c. /

Now this old chap to London would go, / To tell the King a part of his woe ; / Likewise to tell un a part of his grief, / In hopes King George would give him relief. / Right too ra loo ra loo, &c.

Now when this old chap to Lunnun had come, / He found the King to Windsor had gone / But if he’d a known he'd not been at home,' / He dang'd his buttons if ever he'd come. / Right too ra loo ra loo, &c.

Now when this old chap to Windsor did stump, / The gates were barr'd, and all was secure ' / But he knock'd and thump'd with his oaken clump, / There's room within for I to be sure. / Right too ra loo ra loo, &c.

Pray, Mr. Noble, show I the King, ? Is that the King I see there? / I see'd a chap at Bartelmy Fair / Look more like a King that that chap there. / Right too ra loo ra loo, &c.

Well, Mr. King, pray how dy'e do? / I gotten for you a bit of a job, / Which if you'll be so kind as to do, / I gotten a summut for you in my fob. / Right too ra loo ra loo, &c.

The King he took the lease in hand, / To sign it too, was likewise willing ; / And h to make him little amends, / He lugg'd out his bag, and gave him a shilling. / Right too ra loo ra loo, &c.

The King to carry on the joke, / Ordered ten pounds to be paid down / The Farmer he star'd, but nothing spoke— / He star'd again. and he scratch'd his crown. / Right too ra loo ra loo, &c.

The farmer he star'd to see so much money, / And to take it up was likewise willing ; / But if he'd knon he'd got so much money, / He dang'd his wig if he'd give him the shilling. / Right too ra loo ra loo, &c.

The next song in the same collection, "[Major Longbow's Adventures]" (described as "A celebrated Comic Song") has a similar nonsense-syllable chorus—"Tol de rol, &c."—as does a later song in the collection titled "Jack Robinson."

"The King and Countryman" also appears in Burton's Comic Songster (1837). with the same lyrics but with the notation "A popular comic song, as originally sung by Mr. Burton."

A song from The Castle of Otranto (1848), titled "The Cork Leg," which appears in features the chorus:

Right too ro loo ra loo ra loo, right too ro loo ra loo ra loo, right too loo ra lay.

In the scene from Dombey and Son quoted in the posted question, Mr Chick seems to be invoking a chorus from a popular (and comic) music-hall song at a rather inopportune time. I imagine that most of Dickens's English readers in 1846–1848 would have been quite familiar with "The King and Countryman" and similar ditties. Indeed, a letter to Notes and Queries some twenty years later, asking about a missing stanza from the song drew seven responses from various contributors in the August 29, 1868 number of that periodical.