Welder Performance Qualification WPQ:

The essential varibles listed in Section 6 of API 1104 are much different than the essential varibles listed in QW-350-57 of ASME IX.  The one difference that stands out the most is API 1104 Table 3 which requires Nick-Break tests.  ASME IX does not require nick-break tests.  However, API 1104 6.6.1 states that RT may be substituted for the required destructive tests. 
If your welders were qualified using Destructive Tests, then no ASME IX WPQs will not qualify the requirements of API 1104 for Welder Qualification Test Record WQTR. 
If your welders were qualified using RT, then you need to consult API 1104 6 to deterime what your welders are qualified to weld. 
API 1104 has different diameter requirements, and even a branch conection test.  The varibles are much too different to list on a message board. 

WPS:

API 1104 5.3.2.3 has requirements on diameter for WPS/PQR, and ASME IX diameter is non essentail.  ASME IX permits the used of plate to qualify pipe, API 1104 does not.  API 1104 5.4.2.4 has position requirements, 5.4.2.3 has joint design requirements. 
You need to get a copy of API 1104 and really dig into it.  I feel 1104 is much more simple to use that ASME IX, so if you can handle IX, you can handle 1104.  Just don't get them confused. 
They both have very different requirements, and it would not be safe to assume that one qualifies the other.  No one can give you a soilid aswer without your WPS, PQR, and WPQ in front of them. 

Welders, per DOT yes, procedures, no. You have to qualify all procedures as per API 1104
BABrt's