I'm on the fence here. Dd1 was 12 months when they were being changed from them being done at 12 and 13 months to just 12 months.
The reason they changed was to increase vaccination rates. After the 8/12/16 week jabs, parents are less likely to come back for 13 month jab after the 12 month one apparently.
Anyway, I didn't think ds1 was well enough for his jabs so took gp advice on it and they said he was fine. As it was such a new change I was given the choice of together or separate, although strongly encouraged to choose the joint jabs. Given I didn't feel he was up to it, I chose to stay with the 12 month and 13 month schedule.
Ds1 was in hospital just 2 days after his 12 month jab. The hospital were shocked the gp had given him the all clear and said the jab had sent his immune system into overdrive and simply couldn't cope with dealing with an existing throat and ear infection as well as developing immunity to the introduced bacteria/virus.
Naturally when my twins turned 12 months (3 years later), I was so worried about them having the jabs, especially having 2 babies to potentially get ill. But, I decided they hadn't had half the issues ds1 had in his first year so went for it.
Both babies were fine, save a small sensitive area for a day or two. Maybe a mild fever but nothing to worry about, I think one had paracetamol and the other didn't. We also had them done in their legs, two each side. It was best practice then so as to not upset the infant. They don't do jabs in arms at our surgery until the preschool boosters.
So on the whole, I am in favour providing there hasn't previously been mitigating circumstances. You've already said you're not one to be worried so a firm hug and baby will be fine. I think the nurses were always more worried about upsetting the little ones than I was, so make sure the tell them not to worry either. One of mine gave the nurse a big smile after the injection and I swear the nurse nearly bawled she was so happy!