Will Travel Annie soon move into the Washington community that now houses Fannie Mae, Ginnie Mae, Sallie Mae and Freddie Mac?

The possibility was raised yesterday by Discover America Travel Organizations Inc. in a proposal to Congress that a new corporation be formed to market United States tourism to foreigners.

DATO, a trade group for the American travel industry, suggested that the new federal travel corporation would join a select local form of organization known as quasi-government corporations -- all with cute names (Fannie Mae for Federal National Mortgage Association, to cite one example).

The new proposal comes in the wake of President Carter's decision to cut back sharply on government spending to promote tourism in his budget for the next fiscal year.

Testifying before a Senate tourism policy study panel yesterday, DATO President William Toohey said a quasi-government corporation would have independence, flexibility and high visibility -- with a board of 15 members selected by the president and ratified by the Senate.

Noting that foreign visitors spent an estimated $8.5 billion in this country last year, Toohey said the new firm would be designed to organize and administer a comprehensive travel development program to compete more efficiently with other nations for the $156 billion international tourism market.

In his budget message, Carter took the position that promotion should be left to the private sector. Specifically, Carter called for abolishing the U.S. Travel Service as a separate organization in the Commerce Department and consolidating the service with trade activities in the Industry and Trade Administration -- cutting out $11 million of the 1979 travel spending level of $14 million.