Mine get painted by hand ( by Steve the painter ) every time I fancy a change of colour - in my line of work that's quite often !!! It only takes a couple of days ! Worth paying a pro in my opinion ! The finish is brilliant !

The island is very small as shown on your plan, by the time you have a hob installed (roughly 600mm) you will only have 450mm either side of the hob as usable space, also the gaps either side of the island are very narrow, ideally you'd want round 900mm for it to feel comfortable. I would create a U shaped kitchen with a breakfast bar in the centre of the room, that way you still get the island effect you are after but you can keep the units to the right and gain additional units along the internal wall to the bottom of your image as shown.

A melamine faced chipboard door (mfc) would be a very cost effective door and if it gets damaged, its cheap to replace. There's literally hundreds of colours and woodgrains to choose from, suppliers like ba valore, egger, swiss krono, kronospan, xylocleaf, alvic to name just a few, some of the modern laminates are also anti fingerprint, anti scratch and micro scratch repairable (but not for puppy scratches). For a more upmarket premium door, they can be made from solid acrylic (parapan), so in theory scratches can be polished out, doors can also be made using dekton, which is a worktop material made by cosentino that is thin enough to be used as a door facia and is very hardwearing. But tbh, most doors will get damaged by a dog jumping up so i'd be inclined to wait till your dog has grown a bit and calmed down.

Yes a warm wood tone goes beautifully with white. You can choose real wood, porcelain or LVT, a very popular choice on Houzz.