There are a few ways to get a solid background color:

   If you are exporting a PNG, on the File menu, click Document Properties.
   At the bottom of the Document Properties, click Background Color. Change it to whatever you want. Make sure that A (the alpha channel) is not 0. 255 is solid.
   Note: The page background is not a standard SVG feature, so browsers will probably not honor it. Only use this method if you are just converting the the SVG to a PNG with Inkscape.
   Put a rectangle in the background.
   Make sure that the fill color for it is white (I believe the default is transparent) and there is no stroke. This is probably the most browser friendly.