I'm the admin for the board where you originally posted your query. It was off-topic for that board, so I altered the subject line to reflect the content of your post (it previously echoed the topic of the thread you replied to) and moved it to the General board for NZ, where it's more appropriate. I'm posting this reply partly to alert you to where it's gone, and to get the ball rolling on some answers for you...
If you want others to help you further, it could help to know when Robert McDOUGALL was born, and whether he married before he emigrated.
If I were you, the first place I'd start looking would be BDM Online - Historical Records (https://www.bdmhistoricalrecords.dia.govt.nz/Home/
), for his death to start with. This is where it would help to know when he was born, so you can match an age or date of birth.
You can purchase copies of registrations on that site. Be sure to get the printout, not the legal certificate, for family history purposes. (I explain why at http://archiver.rootsweb.ancestry.com/th/read/NEW-ZEALAND/20...
Do check at https://www.bdmhistoricalrecords.dia.govt.nz/dataCollected/
to see exactly what information should have been gathered at the time of the event. Some of the earlier registrations (such as marriages before 1880) don't contain sufficient data to be considered useful to us family historians, so it's a waste of money to buy a copy.
If you don't want to order online, or are dealing with more recent events that aren't on the historical site and don't have an iGovt registration, you can order via ordinary mail - go to Births, Deaths & Marriages (BDM, http://www.bdm.govt.nz/
) and locate the appropriate form. Print the form, complete it with what you know, and send it off with your payment. You can also call and place an order over the phone.
If you are a member of the New Zealand Society of Genealogists (NZSG, http://www.genealogy.org.nz/
) enquire at their Certificates Collection before making purchases at BDM. If they're holding what you're looking for, it is much cheaper. They have lots of other resources for their members, too, so you may like to consider joining if you haven't already, to take advantage of them.
You should also check Archway (http://archway.archives.govt.nz/
), the online index for Archives New Zealand (http://www.archives.govt.nz/
). You may find a probate for him, or some other document of interest that names him.
Anyone can walk into an Archives NZ office and request to view a file they hold. Files are not moved from office to office for your viewing convenience - you have to go to where it is held. Check on Archway for viewing restrictions, and if there are any there will be information there about how to get permission if it is possible.
If you cannot get there yourself, someone else could visit for you. Ask on this board if you need assistance, and someone may be able to go and take photos for you. There should be no charge, as there are no entrance fees and no material costs with emailing digital photos.
Alternatively, you could pay a fee to Archives NZ and they will send you a copy of the file.
You may be able to find his name in a passenger list at https://www.familysearch.org/search/collection/show#uri=http...
If you have access to Ancestry (try your local library if you don't have your own sub) you could look for him in the electoral rolls. Not all years have been indexed yet, so once you've done a search and found him, don't forget to look at the unindexed years.
Hope this helps you along the way. :-)