You didn't disgrace Doctor Who, people draw silly stuff with Daleks all the time.
And you should, it's a fun show. Seems like it would be up your alley. I'd suggest starting with the 9th incarnation of the Doctor (dude with short hair and leather jacket) and then working your way down to the 11th incarnation (dude with suit, bowtie and sometimes cool fez) and THEN going back to the earlier seasons because just starting from the beginning might be overwhelming because not all of the past episodes still exist and there is a LOT to go through. Good times though!