My vet saw my puppies on Friday at 1 week old (coincidentally, we were there for the mother) and said one has an umbilical hernia and to wait and see if it goes.
Everything I am reading online now says these need to be treated, not left.
Not sure whether I should get a 2nd opinion - does anyone have any experience of these and how long they can need to close up, or before I should have another check.

I am sure the others will offer professional advice. Both my dogs have had these the first ones was always obvious but didn't cause her any complications.

This pup had one, the breeder offered me another pup or to cover any vet costs but we stuck with her and it healed. Now at 8 months it has healed completely. I think as long as you have a vet monitoring it and it isn't requiring surgery at this stage you could offer the pup as my breeder did.  My understanding is they can require surgery if very bad. It sounds like you may have to wait it out.

Most umbilical hernias don't need surgery unless absolutely huge, as they tend to fuse in position by the age of 6 months. Inguinal hernias on the other hand are usually more dangerous and more likely to need surgery. I've had 5 dogs (all same breed but not a breed I have now) that had umbilical hernias and they did indeed fuse and so were left alone.

Unless the hernia is very large it shouldn't need any treatment until the pup is neutered (from about 9 months in smaller breeds) when it can be repaired at the same time as the neutering. IMake sure it's reduceable (ie you can push it back into the abdomen) because sometimes the hole in the muscle wall can close to a certain extent and the hernia be improved naturally.

1 week? The abdominal wall has yet to close ...it has to accommodate the now defunct cord structure.
I'd wait and see, most cord stumps take a while to settle and real umbilical hernias seem to truly manifest themselves at around 7-10 weeks.

Vets are a little trigger happy about what often amounts to a tiny bit of fat left behind in a late closure.
The usual sales pitch is " we can neuter at the same time".

>The usual sales pitch is " we can neuter at the same time"

More commonly IME is "we can repair it at the same time as neutering" ie it can wait for a year quite safely.

It depends if it's a true hernia or a late closure (most vets don't differentiate).

I have had the late closure type that trap a tiny bit of fat once the muscle ring closes leaving an outy belly button.

this has never caused a problem including in bitches that have been bred from, and the vet never considered anything needed doing even at time of spaying.

This article may be more useful: http://www.showdogsupersite.com/kenlclub/breedvet/umbilical.html

I agree with Toolz.....many of mine have had a stump at a week....in earlier litters I worried but now having seen often I ignore it and it has always shrunk back 'into' the pup.

Unless it is large I would just monitor and not stress too much.

One of our girls had the same, checked by the vet, no probs. She has had 3 litters with no problems. One of our puppies had the same. I agreed to pay for the op but was not needed. No panic at this stage until at least a year old. Please do not neuter until at least 18 months, puppies need the hormones to mature correctly.