AmE stands for American English. We also use BrE for British English.

In your example, it's the coordinator "and" which is typically omitted in AmE, but included in BrE:

We should go pay the doctor a visit. (AmE)
We should go and pay the doctor a visit. (BrE)

There are also certain other expressions where a preposition is omitted in AmE but not in BrE, for example:

He jumped out the window. (AmE)
He jumped out of the window. (BrE)


See what I mean?

PaulM