It is possible that your last cycle was implantation bleeding, but you really won't know exactly how far along you are until you have an ultrasound. I don't think it matters how fast your positive shows up. Mine showed up right away with DD2 and it was 9 days before my period was due.
I thought I was about a week further this time than the due date calculator said, and I was close. I was 5 days further than my last period said I should be. Unfortunately, you're probably gonna have to wait until your first appointment to know for sure. Congratulations and good luck!