Can an i-Mac monitor (2019) be plugged into a MacBook to provide a larger screen?

No. The 2019 iMac does not support Target Display mode natively.

She could use a number of third party alternatives such as LunaDisplay to use the iMac as a display for another Mac though, but those can introduce lag and other issues so are not suitable for video editing or high paced games, but can work for things like Word Processing, email and web browsing pretty well.

https://astropad.com/blog/step-by-step-guide-how-to-use-your-imac-as-a-monitor/

Grant Bennet-Alder wrote:

Read that article with Caution.

The article Phil0124 cited is not an impartial review by a disinterested third party.

It is an advertorial by Astropad, the maker of Luna display.

Even that article acknowledges that

"Like any product, Luna Display does have limitations and it’s not recommended for high-motion content. For example, I wouldn’t recommend using Luna Display for gaming or video editing.

Since Luna Display is squeezing a 5K display through a USB cable, when lots of motion occurs on-screen (like from video playback or moving a window quickly) the screen can temporarily become pixelated before it renders in at full resolution."

what the Luna Display hardware does is to capture the high speed display output and hold it in its external screen buffer. It then sends the essence of the captured display information, but far more slowly, across your Home network to a remote machine, such as an IMac. This is FAR short of full motion Video.

But you can do something similar by 'Sharing' [in this context, "make available for use by others"] the MacBook Air built-in screen. Then use Screen Sharing in the iMac to display that information In a window on the iMac running any supported version of MacOS.

Turn Mac screen sharing on or off - Apple Support

For this use, the iMac can run any version MacOS 10.14 Mojave to MacOS 15 Sequoia.

The faster the network connection for BOTH computers, the better the results.

Share the screen of another Mac - Apple Support

There is another potential pathway to a very similar result. That is by using Airplay. Airplay has stricter requirements and limitations:

To use AirPlay on a Mac, you need MacOS Monterey (12) or later, and compatible hardware such as a MacBook introduced in 2018 or later, or an iMac introduced in 2019 or later.

These articles lean heavily on streaming to an iPhone or iPad, but this can be generalized to an appropriate Mac, and to an Ethernet or mixed network instead of all Wi-Fi.

Use AirPlay to stream video or mirror the screen of your iPhone or iPad - Apple Support

Read that article with Caution.

The article Phil0124 cited is not an impartial review by a disinterested third party.

It is an advertorial by Astropad, the maker of Luna display.

What model-year MacBook Pro as source?