There's not really a good way of copying labels from a PDF of a map into QGIS. Here's how the process will work if you try it:
- Add the PDF to QGIS. Use the georeferencer tool to georeference it. Here's a tutorial.
- Create a new point vector layer. Add a new text field to the attribute table. Make sure the new field is long enough to hold the longest possible label.
- Set the symbology for this label to 'no symbol'. Turn on labeling, using the field you created in step 2.
- Digitize a point on top of each label on the georeferenced PDF. As you add each point, type the label text into the attribute table field.
- To move a label, turn the point symbology back on and use the
move feature
button. Or if you need tighter control over label placement, use the tools in the Labels toolbar to move the individual labels.
- Create a print layout with your labels in it. Make sure the map object has transparent background. Export as a PDF.
Import the PDF into Illustrator, and discover that PDFs produced by QGIS do not play nicely with Adobe Illustrator. Futz around with the layer in Illustrator until you either:
a. Figure it out and make it work, or
b. Give up and create the labels in Illustrator, kicking yourself for not doing it this way in the first place.
I strongly recommend making a small test layer with a few dummy labels, and skip straight to step 6-7 (trying to make it work in Illustrator). If you can't make it work in Illustrator, don't waste your time on steps 1-5.
If you do figure out how to make a PDF from QGIS work in Illustrator, please post an answer with detailed instructions (so I can tell my boss how to do it and she can stop yelling at me about why my maps don't work when she tries to "fix" them).