Neil Pickup said:
All it takes is a bit of effort...
Qasim Umar (Pak, 26 Tests, 1983-86) - RHB
William Quaife (Eng, 7 Tests, 1899-1902) - RHB
Qaiser Abbas (Pak, 1 Test, 2000) - LHB/SLA
+Javed Qadeer (Pak, 1 ODI, 1995) - RHB/WK
Mehmood Quaraishy (EC Africa, 3 ODIs, 1975) - AR
Akhlaq Qureshi (Italy, 5 ICCT, 1997) - RHB/RM
*Abdul Qadir (Pak, 67 Tests, 1977-90) - LBG
Iqbal Qasim (Pak, 50 Tests, 1976-88) - SLA
Neville Quinn (SA, 12 Tests, 1929-32) - LFM
Pamela Quin (Sco, 1 WODI, 2001) - RHB
Qanita Jalil (Pak, 4 WODIs, 2005-2006) - RMF
This is not meant to be a mixed team, involving women.
You could have gone with these players -
Quintin McMillan (SA, 13 Tests, 1929-32) - LBG/RHB
Eric Quail Davies (SA, 5 Tests, 1936-39) - RF
And on a search, there are many more players having their name start with a "Q", but they only officiated in international matches and not played them.
The team currently becomes -
Qasim Umar (Pak, 26 Tests, 1983-86) - RHB
William Quaife (Eng, 7 Tests, 1899-1902) - RHB
Qaiser Abbas (Pak, 1 Test, 2000) - LHB/SLA
+Javed Qadeer (Pak, 1 ODI, 1995) - RHB/WK
Mehmood Quaraishy (EC Africa, 3 ODIs, 1975) - AR
Akhlaq Qureshi (Italy, 5 ICCT, 1997) - RHB/RM
Quintin McMillan (SA, 13 Tests, 1929-32) - LBG/RHB
*Abdul Qadir (Pak, 67 Tests, 1977-90) - LBG
Iqbal Qasim (Pak, 50 Tests, 1976-88) - SLA
Neville Quinn (SA, 12 Tests, 1929-32) - LFM
Eric Quail Davies (SA, 5 Tests, 1936-39) - RF