Rsyslog filter not working

I am on debian 10 and I'm trying to do a very simple thing with rsyslog : I would like to redirect all logs from a particuliar docker container into a log file.

I set a tag to my docker container, and the log driver to "syslog" so now, in my journalctl I can see such lines :

Sep 25 18:34:05 XXXX my_docker[18678]: XXXXXXXX

Great. Now I want to redirect those lines to a log file (the goal is to use fail2ban).

I created a new file /etc/rsyslog/mydocker.conf with the following content:

if $programname == 'my_docker' then /var/log/my_docker.log

I also tried :

:programname, equals, " my_docker"  /var/log/my_docker.log

Then I did a simple

systemctl restart rsyslog

And… Nothing !
The file is not created (even though, when I make a journalctl -t my_docker -f I can see logs spawning).

I also tried the following :

• Put the filter directly into /etc/rsyslog.conf
• Manually touch the /var/log/my_docker.log file with 777 mode

And nothing works !

Here is my /etc/rsyslog.conf :

# /etc/rsyslog.conf configuration file for rsyslog
#
# For more information install rsyslog-doc and see
# /usr/share/doc/rsyslog-doc/html/configuration/index.html


#################
#### MODULES ####
#################

module(load="imuxsock") # provides support for local system logging
module(load="imklog")   # provides kernel logging support
#module(load="immark")  # provides --MARK-- message capability

# provides UDP syslog reception
#module(load="imudp")
#input(type="imudp" port="514")

# provides TCP syslog reception
#module(load="imtcp")
#input(type="imtcp" port="514")


###########################
#### GLOBAL DIRECTIVES ####
###########################

#
# Use traditional timestamp format.
# To enable high precision timestamps, comment out the following line.
#
$ActionFileDefaultTemplate RSYSLOG_TraditionalFileFormat

#
# Set the default permissions for all log files.
#
$FileOwner root
$FileGroup adm
$FileCreateMode 0640
$DirCreateMode 0755
$Umask 0022

#
# Where to place spool and state files
#
$WorkDirectory /var/spool/rsyslog

#
# Include all config files in /etc/rsyslog.d/
#
$IncludeConfig /etc/rsyslog.d/*.conf


###############
#### RULES ####
###############

#
# First some standard log files.  Log by facility.
#
auth,authpriv.*         /var/log/auth.log
*.*;auth,authpriv.none      -/var/log/syslog
#cron.*             /var/log/cron.log
daemon.*            -/var/log/daemon.log
kern.*              -/var/log/kern.log
lpr.*               -/var/log/lpr.log
mail.*              -/var/log/mail.log
user.*              -/var/log/user.log

#
# Logging for the mail system.  Split it up so that
# it is easy to write scripts to parse these files.
#
mail.info           -/var/log/mail.info
mail.warn           -/var/log/mail.warn
mail.err            /var/log/mail.err

#
# Some "catch-all" log files.
#
*.=debug;\
    auth,authpriv.none;\
    news.none;mail.none -/var/log/debug
*.=info;*.=notice;*.=warn;\
    auth,authpriv.none;\
    cron,daemon.none;\
    mail,news.none      -/var/log/messages

#
# Emergencies are sent to everybody logged in.
#
*.emerg             :omusrmsg:*

I searched for a while, read the doc several time and I don't understand where it can go wrong in such a simple setup !

Thanks !