There are two fabrics that I could be used for the velvety feel in a quilt that would survive washings well:
(Although I'm not sure about current availability - these are fabrics in my stash)
Brushed arnel - remember that stuff that robes used to be made of? Only thing that wrecks this stuff is very high heat - as in a burn - or cuts - very abrasive resistant and washes very well.
Cotton velveteen - behaves a lot like cotton corduroy.
How about a very fine wale cotton corduroy?
Preshrinking is a must for a baby quilt (In my opinion)
For shiny - I don't know. There may be some polyester satins out there. I obtained some satin from my Mom - who got it at a garage sale - that I washed in HOT water (not the best thing to do - but I was going to make it into pillow cases and I wanted to know what it would do) and it survived nicely. I even ironed it on low cotton setting with full steam.
If you are going to do stunts like that - do it on a small piece first so you don't wreck the whole chunk of fabric. I didn't have much invested in this piece, so it was kind of a "whatever happens, happens" thing.
I would recommend washing in warm or cool water (generally not much warmer than body temperature).
Back to the satin - it FRAYS and/or RAVELS. So you would either have to leave wide seam allowances or put fray check on it, or overcast/serge it to keep it from pulling out.
Sturdy satin does work - my grandchildren had satin pillowcases that they loved to shreds.