I wash every quilt I make before it goes anywhere - to me, it is not complete until it's survived a wash and dry, lol. For a baby quilt, I'd wash it in a baby detergent (which I always have, because I have children with sensitive skin, but I like my own nice scented detergent, so I do our laundry separately), but if you don't have baby detergent, I'd just wash and tell the mom what you used should she wish to re-wash in her own detergent, giving washing instructions.
Actually, I would *especially* wash a baby quilt because I use so much "crap" putting them together...starch, 505, Elmer's...it NEEDS to be washed before going near a teeny baby. :)
Edit...Oh! Just re-read - DON'T wash the top before it's quilted! Put it all together first, bind it and then wash. If you are concerned about the colours running, I hear Shout Color Catchers are great, never used them myself.