Shodan (1st Dan) really means beginning level not Mastery but in any case I never get wrapped up in comparing what one blackbelt means to another.
I totally agree with this. 1st Dan shouldn't be as big as deal as it is sometimes made out to be. Secondly, one and a half year may be quite realistic to get to Shodan. It all depends on how much training hours you put in and how actively you're being taught/coached by the teacher and other dojo members. I mean, if you get individual (and correct) feedback on every technique you practice in a class, you can progress quite rapidly. Unfortunately practical consideration prevent that from happening.