Did you search? I found Barker Cabinets through here, and they seem ideal for your application (3/4" plywood boxes should hold anything up).

The majority of RTA cabinets on the web are Chinese. With dealers that don't last more than a year selling them. Barker, Scherrs, and Conestoga are 3 exceptions. Do your research. You won't be saving that much money for a small order over buying from a cabinet company that will also sell vanities. Shenendoah, or American Woodmark at the box stores can do a pretty decent vanity for not much money. Aristokraft from a cabinet company also is decent quality.

I looked up Barker, Scherrs, and Conestoga and I couldn't find any white vanities on their sites.
I can't afford even the Shendendoah or American Woodmark type vanities, believe it or not. They start a $300-$400 for a small vanity. I can get a solid wood, painted RTA one for $200. I found a local dealer that had one in the size I needed in stock and he will assemble it for $10! I think I may go with that, unless someone has any good warnings about something I may not have thought of. It is by J & K cabinets, btw.
Thanks!

On the Barker site you just have to select the options. You can get them unfinished, clear varnish or one of two white paint colors.

I have used both Conestoga and Barker. The quality is high, the service is great. In the hands of a good DIY or contractor, they can be quickly assembled. The disadvantage of Barker is you need to stain yourself. I like staining and finishing but not every homeowner does. I will also confess that when facing 26 shelves I farmed out the work to our painter once I had the stain mix perfected.

Thanks everyone. Well, I found out that J & K cabinets (a large RTA cabinet distributor) had a local dealer not too far from me, (Global Home Products in Beltsville, MD) so I called them and they actually had the size and color vanity I wanted in stock. The price was $199, and assembly was only $10, for an all wood, painted white shaker style vanity. Even the center panel on the doors was solid wood --a true reverse raised panel (almost every RTA cabinet seems to use MDF for the center panel!) The cheapest, similar, special order cabinet from Home Depot or Lowes would have been between $300-400 (American Woodmark or Kraftmaid, etc.) I checked with Barker cabinets and they were quite expensive in comparison.

When I got to the dealer, I was surprised to see what a large showroom they had and how busy they were, even on a weekday afternoon. I believe that all their cabinet lines were RTA, and they had very good prices. The display kitchens and vanities looked very nice. The place seemed to be run mainly by Chinese people, ( a little hard to understand their accents, but very nice and helpful) so I imagine they don't have any problems communicating directly with those factories that make their cabinets over in China if they need to!
Anyway--I'm glad that I had them put the cabinet together, as when they opened the box there was some minor damage to the face frame part. So they used the face frame off the identical vanity that was on their showroom floor and were able to assemble my vanity. It does look gorgeous--esp. the doors.
Even the back is solid plywood with wood bracing. I suppose that makes it more sturdy, but it will be more work for my husband to drill holes for the plumbing.
Hope this helps someone else who might be wondering about RTA cabinets.

@fun2learn I am interested in J&K cabinets for my kitchen. How has the cabinet held up? Do you find the wood is easy to ding or dent? Have the door hinges or drawer rails started to stick or fail?