Now we've set up an identical Website on a new similarly named domain that better describes our business - example: BusinessNameRestaurant.com became BusinessNameBanquets.com. Later we'll discontinue the first domain.
I'm worried about moving our landing pages over to the new domain, since G has no history of it and probably hasn't even crawled it yet.
Is that a good thing to do?
This means that you will have 1 advert for your old domain and 1 for the new domain. Let the ads run for a while and see which one people favour, it could be that your new domain actually increases CTR for the people you want to attract.
The important part of this is not to delete the old advert until your new one is working well, if you can let the two run together for a month or more you should be fine, but I would let them run simultaneously for as long as possible.
You need to go to the adgroup and then click the 'Ad Variations' tab, then click 'Text ad' next to Create New Ad:. This lets you add another advert in the adgroup (that advert can be to a different domain), thus keeping your history.