Update
Well, the site didn't make it out of private beta. So that's an easy way to answer this question :)
Original Post
Right now: no. We literally can't, migration into private betas is blocked by the migration system.
If Web Design makes it to public beta: maybe, but probably only if the question is closed as off topic on Graphic design. This is explained in a Stack Exchange blog post from a couple years ago: Respect the community – your own, and others’.
Here's the relevant bit:
Respecting your own community
As members of a community, your first loyalty should be to that
community. When evaluating a question, you shouldn’t be looking to
push it off on some other site; instead, ask if it could be
appropriate and on-topic for you, the experts who the author decided
to ask. Be a bit jealous of your site – don’t blithely turn askers
away simply because their question could be asked somewhere else.
Don’t hit them over the head with your scope, help them tailor their
question to fit into it – and if that means your site’s scope overlaps
a bit with another site’s, so be it.
Obviously, there are questions you’ll have to turn away, either
because their only connection to your site is via the audience (“How
do I make bread as a programmer?”), because it’s completely off-topic
(“How do I cook a fish in a dishwasher?” obviously belongs on Cooking,
not Home Improvement) or because they’re simply not useful or
constructive. But that should be your last resort. Close questions
with an eye toward improvement and re-opening, not driving users away.
The other thing to keep in mind here is to not migrate crummy questions. If it's just a straight-up no effort post, it's not worth migrating. For smaller sites I will typically get in touch with the community or mods on the receiving site and confirm the migrating with them beforehand.
Respecting other communities The migration tool was created to help those unfortunate users who asked good questions on the wrong site. Do
your best to remember this, whether as a user (flagging or voting to
close) or as a moderator (responding to flags).
- Don’t migrate poorly-asked or non-constructive questions. Just close them. If you want to help the asker out by recommending a site
where their question would be on-topic, go ahead – but also recommend
they read that site’s FAQ first!
So in short: yes, if it's a quality question that is consider off-topic on our site but within the scope of Web Design.
