More than one way to resolve this. You can take the handle off, but the shaft of the stem will still be sticking out a fair ways.
You could take the valve off (after shutting the water off, of course), slid the old one off and set the new one over it. Or, you have enough sticking out where you could just cut the old one off and then install a new one on what's left after you have the new vanity in place.
Or, once you have the old one out, you could move the line either to the wall or at least back so it could come up through the back edge in a U-shaped hole, rather than a through hole in the middle.
I can't tell for sure, but is that valve threaded on? If so, it will just unscrew. There's what looks like a plastic ring...it may also be just a push-on connection.
Probably other ways, too, but you get the idea.