How to create a portrait video for IGTV?

I have a regular/classic landscape orientation timeline at 1080x1920 and I would like to know if I can either create a copy of this timeline in 1920x1080 (ie Portrait orientation which then can be viewed in landscape when you turn your phone on its side) or export it to these dimensions and somehow rotate the footage at render.

I don't fully understand your question. So, your final result will be shown upright, yes?
Is your original footage upright or on the side? You can always rotate any clip in the Inspector and you can generate a custom timeline with the dimensions you are asking for.

I have a regular/classic landscape orientation timeline at 1080x1920 and I would like to know if I can either create a copy of this timeline in 1920x1080 (ie Portrait orientation which then can be viewed in landscape when you turn your phone on its side) or export it to these dimensions and somehow rotate the footage at render.

Here is a video that might help.

You can adjust the ratio of your video. If you're shooting your video in landscape mode, you'll need to change the ratio to 9:16 and thus the video will become vertical.