My guess is this is not possible through the API ( and thus the new-naqtree cmdlet). I don't see a way to get this to work.
However, there is a workaround. Try:
$qtree = "/vol/$volumename`/$qtreename"
Invoke-NaSsh "qtree create `"$qtree`""
One other note, is the storage management guide recommends against using certain characters (namely, spaces and commas) in QTree names for various reasons, including that it breaks SnapMirror:
Qtree name restrictions
Using some special characters in qtree names, such as commas and spaces, can cause problems with
other Data ONTAP capabilities, and should be avoided.
The following characters should be avoided in qtree names:
• Space
Spaces in qtree names can prevent SnapMirror updates from working correctly.
• Comma
Commas in qtree names can prevent quotas from working correctly for that qtree, unless the name
is enclosed in double quotation marks.