Greetings Jim, and Welcome to Chordie!
Honestly I don't know what the spacing should be on your Mando, but just thinking about it the spacing you presented sounds close to me.... it can vary by instrument model and maker, and depends on the nut width.
Spacing between pairs of strings is only relevant if you are picking more than one course of strings at a time, and that is up to the style of playing your are attempting. Four courses of two strings each on a petite neck such as a Mandolin really eats up the real-estate on the fretboard, and it is easy to see that overlapping could be a real issue with those of us with "fat" fingertips. I know that it was a real problem for me early in my playing with a twelve string Guitar.... at least up to the point that my calluses got hard enough that the tips quit flattening out. Trimming the nails really short on the fretting hand also helped a LOT!
There are a few Mandolin players in the group here that I'm sure will chime in with tidbits of info to help you get around this, but I see you are new to Chordie and wanted to Welcome you to the Community. It's a fine bunch of folks around here and it is nice to have you aboard.
Take Care;
Doug
"what is this quintessence of dust?" - Shakespeare