Fleming is leaving after four and a half years at the helm of the outspoken group's comms to join Penrose Financial institutional team as an account director in two weeks' time.
Dawson joined Moneyfacts in 1996 as a researcher and later became deputy editor of Moneyfacts' subscription-only publication Business Moneyfacts. She became head of press and PR in 2004 and has been replaced by Moneyfacts press officer Andrew Hagger, who is now head of news and press.
Along with the Association of British Insurers (ABI), the NAPF has been one of the more visible faces of the UK fund management industry over the past few years.
In particular the body, whose members manage around one sixth of the shares of FTSE 100 companies, has been particularly vocal on corporate governance and pension reform.
Earlier this month the NAPF unveiled its alternative to Lord Turner's proposed National Pensions Savings Scheme.
The NAPF said a network of up to 20 investment trust-style vehicles should be set up to hold the assets of workplace pension schemes, each with their own independent board.
NAPF chief executive Christine Farnish said the trusts would be large enough to deliver economies of scale and would ensure costs were kept low due to market competition.
Fleming joins Penrose's institutional team following the promotion of Ben Curson to the Penrose board.