Democrats hiking the early trail on the climb to the presidency have already reached their first pique: a high-level squabble that erupted when Gov. Edmund G. (Jerry) Brown Jr. passed the word that he was endorsing fellow Californian Sen. Alan Cranston's candidacy and Sen. Edward M. Kennedy passed the word that he was displeased.

It happened in Philadelphia, in a private exchange of telephone calls between the principals, while the Democrats were publicly putting their most fraternal faces forward at the party's mid-term conference in late June. And it indicates just how thin is the skin of Democratic unity, and how intense is the one-upmanship in the 1984 presidential contest, which is still two years away.

The disquietude began on the opening night of the conference. While the candidates were publicly visiting each other's cocktail parties and exchanging best-wishes, Brown telephoned Kennedy and former vice president Walter F. Mondale from Sacramento.

He told them, according to advisers to all involved, that he was going to Philadelphia to hold a press conference with Cranston to proclaim--with appropriate media fanfare--his endorsement of his home-state colleague's presidential campaign, which Brown had done last March, in a press release that received only scant attention.

To Brown, who needs all the California support he can get for his own U.S. Senate campaign, it seemed like smart politics. To Kennedy, it seemed like upstaging. So he responded with distinct displeasure.

According to Democratic sources outside the Kennedy camp, Kennedy warned Brown that if he went through with the Philadelphia press conference, Kennedy might find it very difficult to go to California and campaign for Brown, preferring to campaign for his true political friends instead.

Kennedy then called Cranston, who was in a hotel suite in Philadelphia, and repeated what he had just told Brown. Then, for extra measure, Kennedy's administrative assistant, Lawrence Horowitz, telephoned Brown's campaign chief, Michael (Mickey) Kantor, and made the same argument, Kennedy's spokesman, Robert Shrum, said.

He said Kennedy was not really angry and never meant to voice a threat, just some political facts of life.

"He Kennedy was trying to make an argument on why Brown should not go through with" his press conference endorsing Cranston, Shrum conceded. ". . . . What he Kennedy said was, 'If you do this you make it more difficult for me in terms of the other people who supported me in 1980,' " some of whom Kennedy is telling he does not have time to campaign for this year because of his own Senate reelection campaign.

Kennedy's spokesman said his boss also told Brown: "I have got to campaign in Massachusetts and I only have a limited amount of time."

Mondale, meanwhile, took a different tack. He expressed no objection.

What the former vice president told Brown, according to a Mondale aide, was basically: "Jerry, I understand what you are doing. I understand you are running for the Senate and that comes first, and that Alan is enormously popular in California."

The aide said Mondale promised to go and campaign for Brown's Senate race and that he added: "If Alan turns out not to be in it the presidential race at the end, I'd like to talk to you about the possibility of your supporting me."

The next day, however, a budget crisis and a Mediterranean fruit fly were discovered in California almost simultaneously, causing Brown to hastily cancel his trip to Philadelphia. The crises were real, a Brown adviser said, and Brown did not scrub his plans because of his talk with Kennedy. Instead of a joint press conference, Brown and Cranston put out a joint press release declaring Brown's support for Cranston, an action that received only scant attention in the press.

Finally, last Friday, Kennedy and Brown made political peace, aides to both men said. Brown telephoned on Monday but missed Kennedy, who got around to returning the call on Thursday but missed Brown, who in turn tried again a day later and scored.

They agreed that Kennedy would go to California on Sept. 24 for a previously scheduled event sponsored by the AFL-CIO.