First of all: What the manual says?

Next it seems that DX3000 has no own Hamlib model 132 is for DX5000 so it might not work in all cases.

When cqrlog is running start telnet in command console and give command "\dump_caps"
You get long list what the rig can do. There, near the end is "Can send morse"
It must be "Y"

If it is Y and your rig is on CW mode try next type command:

b de sp6ina

you should get rprt0 and CW out from DX3000
if it works the Hamlib can send CW.

next give
Q
to get out of telnet.

[saku@hamtpad ~]$ telnet localhost 4532
Trying 127.0.0.1...
Connected to localhost.
Escape character is '^]'.
\dump_caps
Caps dump for model: 373
Model name: IC-7300
Mfg name: Icom
...
....
....
Can send Morse: Y
Can decode Events: Y
Can set Bank: N
Can set Mem: Y
Can get Mem: N
Can set Channel: E
Can get Channel: E
Can ctl Mem/VFO: Y
Can Scan: Y
Can get Info: N
Can get power2mW: Y
Can get mW2power: Y

Overall backend warnings: 0
RPRT 0

b de sp6ina
RPRT 0

q

If that was ok then start cqrlog from console with command:

cqrlog debug=1 > /tmp/debug.txt

Try to change preferences CQ interface to "none" close preferences then go back and set it back to Hamlib and close preferences.
Then try to send a CW macro and close cqrlog (if CW does not work, otherwise use it and be happy...).

Next add file /tmp/debug.txt to your next message so we see what happended when you switched CW keyer to none and back to hamlib and tried to send a CW macro.