Hi sheri, welcome to Affinity Forum.
I am a graphic designer with a strong pre-press background.
Would you be able to upload the AD file you are needing to export?
Without actually seeing how your file is constructed, I'll assume that there are no special 'effects' in it that might rasterise when exported.
For text frames & art text, it pays to convert them to curves prior to export.
I work with Adobe Creative Suite, CS5 for my employer - InDesign, Photoshop & Illustrator.
I have found that the best way to retain the vector paths in AD, when exporting for Illustrator, is to export to PDF.
Having said that, if I have applied any raster filters, shadows, bitmap fills, the vector shapes end up being rasterised!
Best regards,
Paul.