A runner???

So, on Thursday I ran my first "race".  I only say it like that because there was no actual winner or loser, just a bunch of runners out running for fun.  Anyway, I thought it was a really good way to break into the running scene.  I did really well, considering it was a 2K.  I finished with a time of 15:18, which was my fastest to date.  So I decided that maybe I need to try to do less walking intervals so that eventually I am just running without any walking at all, and I want to increase my distances. Today while out running with Matt around the neighborhood, I started to think about all of this running I am trying to do.  I just got to wondering if avid runners laugh at people like me.  I mean some people go out and run like 10 miles a day and here I am with my measly 1.25 or 1.5 miles a day and I am dying.  So, I wonder, should I just jump in and try running like 3 miles, or should I keep doing what I am doing and take it slow?  I think I have been doing pretty well considering I have only been running for about a month or so and that I am still heavy.  I think I will just keep chugging along and see where this all takes me.  I was actually feeling pretty good after my run today.  For a quick 18 minute run I only walked at total of about 2 and a half minutes.  My goal by the end of July is to run without any walking intervals.  Here's to running without stopping!!!