Why don't you call a few local landscape architects or civil engineers to see what their fees would be for such a project?

There's not enough information here to tell. If you pretty much have a viable plan, getting one to draw up acceptable plans for submission and putting his stamp on them probably will run a few hundred. If he actually has to do engineering rather than just blessing yours, it will run more.

I can give you two recommendations based on experiences I've had over the years.

First, GET SOMEONE WHO HAS DONE SUCH A SUBMISSION IN YOUR COUNTY (or whatever municipality is doing the plan review). I had a complete disaster of a submission because I didn't check that. All it turned out costing me was time (took me many interations). The only good thing I could say was the groups was so incompetent they never realize I hadn't paid them either.

Second, as with any personal service like this be it an architect or engineer or contractor or even a dentist: GET RECOMMENDATIONS. Especially from a source you trust. Get multiple bids. You'll get an idea from that as well.