Her two autobiographies might contain some info. Her first year may have been as early as 1958!
What follows comes from World Tennis and covers 1960 to late 1964
Court's titles by year.
*Until 1967 she played as Margaret Smith
*Final opponent, date and score given when known.
1960
Aussie: d. Lehane
Queensland: (Nov 5) d. Turner 10-8 6-1
1961 13 titles known
This was the year Mags was on an official tour with other Aussie girls.
Adelaide: (Jan14) d. Lehane 6-3 6-0
Aussie (Jan 27) d. Lehane 6-1 6-4
Paris: (April 4) d. de la Courtie 6-1 6-3
Nice: (April 9) d. de la Courtie 9-7 6-4
Provence (April 16) d. Starkie 6-2 6-4
Monte Carlo (April 30) d. Starkie 6-4 6-1
Beckenham: (June 17) d. Truman 6-3 4-6 8-6
Queen's Club (June 26) d. Richey 6-0 4-6 6-2
Aussie Hard: (Oct 23) d. Turner 6-2 0-6 7-5
Adelaide (Nov 25) d. Hard 6-4 5-7 6-4
Perth, West Aussie (Dec 4) d. Hard 6-3 6-0
Victorian: (Dec 9) d. Hard 6-3 6-2
New South Wales (Dec 17) d. Hard 6-2 6-1
1962 Won 13 known events
The year of the great fight between M and the Aussie LTA. She toured privately and was shunned by the official Aussie women's team. She is undefeated from sept 61 until the QF of Manchester in June 62, at least 9 straight events won.
Aussie (Jan 15) d. Lehane 6-0 6-2
Italy (May 15) d. Bueno 8-6 5-7 6-4
Lugano (May 21) d. Turner 6-2 6-1
French (June 4) d. Turner 6-3 3-6 7-5 (survives mp)
Bristol: (June 16) d. Bueno 6-1 3-6 6-2
Penn Grass, Merion (July 30) d. Susman 6-4 10-8
Orange (August 6) d. Susman 6-3 6-4
Essex (August 19) d. Bueno 6-1 6-4
US Nationals (Sept 10) d. Hard 9-7 6-4 (Hard bursts into tears during F)
Queensland (Oct 28) d. Lehane 6-3 6-4
Adelaide (Nov 17) d. Truman 6-1 6-2
NSW: (Dec 1) d. Turner 8-6 6-2
Victorian (Dec 15) d. Turner 6-4 8-6
1963 Won 14 known events
Aussie (Jan 19) d. Lehane 6-2 6-2
Italy (May 14) d. Turner 6-3 6-4
Berlin (June 3) d. Ebbern 6-2 7-5
Barcelona (June 9) d. Turner 6-0 6-0
Beckenham (June 16) d. Lehane 6-0 6-1
Wimbledon (July ?) d. Moffitt 6-4 6-4
Dusseldorf (July 14) d. Turner 6-3 6-2
Orange (August 4) d. Hard 6-1 6-1
Essex (August 14) d. Bueno 6-4 11-9
Queensland Hard (Oct 19) d. Ebbern 7-5 6-2
Queensland (Nov 7) d. Turner 6-3 6-2
NSW (Nov 7) d. Tegart 6-1 6-3
Adelaide (Nov 18) d. Lehane 6-3 6-1
Victorian (?) d. Turner 6-4 6-4
1964
*Court only lost 2 matches all year-once to Bueno (Wimbledon final) and once to Susman (4R US Nationals). This is probably the best won-lose percentage after Navratilova's amazing 1983, when Martina dropped only one match.
Aussie (Jan 13) d. Turner 6-3 6-2
Auckland (Feb 9) d. Lehane 6-4 3-6 6-0
Reggio Calabria (May 3) d. Ebbern 6-0 6-4
Italy (May ?) d. Turner 6-1 6-1
Berlin (May 18) d. Schultze 6-2 6-1
French (May 31) d. Bueno 5-7 6-1 6-2
Beckenham (June 13) Shared title due to rain. Led Bueno 5-3.
Queen's Club (June 20) d. Jones 6-3 6-2
Hilversum (July) d. Bueno 6-0 1-6 6-3
Gstaad (July 17) d. Turner 6-4 6-2
Hannover (August 2) d. Pachta 6-0 6-1
German (August 11) d. Bueno 6-1 6-4.
More coming-let us know what other titles she has!