It's great to have you as part of the community. Welcome to Workshop. I'm looking forward to reading more about your projects.
We did something similar to what you are planning at our house as part of a major renovation. We had an existing concrete slab at the back our our house that we needed to work with as removing it would have added considerable expense. We put a deck over it but it affected the levels in the house - we had to find a logical place for a step somewhere. It's never easy working with existing structures! We needed an architect and a professional builder in our case, but hopefully you can get the assistance you need and avoid that expense.
It's certainly something that can be done by a competent DIY'er, and not only will it save you money, the satisfaction of having done it yourself will be worth even more.
When you say "ordering custom timber materials", what do you mean? Most timber for a job such as this would be ordered in specific sizes (140 x 45, 190 x 45, 90 x 90, etc.) to span a particular job (posts, rafters, end beams, etc.), then ordered by enough length for you to cut to size for the job. Do a google search for "Timber Span sizes for Pergolas" and you'll find a heap of helpful technical info.
A couple of other things to consider. Check with local council about whether a building permit would be required. If the existing structure already had a permit, you may be able to "repair/rebuild" the old one without having to obtain a permit for a new build. Secondly, a freestanding structure will require more bracing support than one attached to a dwelling, and therefore careful design planning will be required.
Just checking in to see how you are going with your patio project. Have you made any progress?