Ask away, it's fine 
We didn't do a food sensitivity test first I just decided to do it. We did see a paediatician several months into the diet about intolerances. He said they can't reliably test for intolerances only allergies, and that cutting one thing out at a time was the best way to see if it was causing problems. You used to be able to send frozen urine samples to the university of Sunderland and they would check for peptides I think indicating sensitivities ( for £60 ) but I don't know how to go about this-someone else might know?
I knew DS was dairy intolerant as whenever he had a tiny bit it upset him. Gluten I guessed as even without dairy his poos smelled wrong, v acidic smelling and unhealthy looking (I used to work in colorectal surgery so had many previous dealings with poo 
)
I didn't go through the GP. Ours know very little about ASD/gut problems particularly in children with ASD, as far as I can tell. I have mentioned probiotics to them and they do not really have a view on them, interestingly though at the request of a friend I accompanied him to his child's ASD assessment and the community paediatrician recommended considering probiotics so they're becoming more recognised as having a place and "mainstream" I think. In the Czech Republic they give them to children alongside antibiotics to combat the negative effect ABs have on gut flora.
You could ask a nutritionist/dietician to advise you, they could give you ideas on doing things slowly etc.
DS hasn't had milk at all since I gave up breastfeeding at 15 months. DS isn't a yoghurt man, and i think almond milk is regarded as being gentler on the gut, but my friend's son is fine with soya yoghurts etc so I would say they'd be fine as long as your DS will eat them and they don't upset his tummy. People who do the GAPS diet wouldn't allow soya but full GAPS wasn't an option for us due to DS's limited diet, and other parents I've chatted to hold the view that cutting out gluten and dairy alone has been enough to help their children. You could try putting a little bit of almond milk in with your DS's usual milk then slowly increasing the ratio.
Does your DS have any gut problems at all? Are school supporting your DS well?
I decided it didn't matter what DS ate to start with as long as it was gf/cf something, then I'd work on getting more healthy as time went on. His appetite is much better now he's been gf/cf for 7 months or so.
I try to put different foods on the table/within his general reach and just hope he will try them-occassionally he will.
If you don't mind being stealthy you could transfer gf bread into your usual packet (making sure all crumbs/traces from usual loaf are out) and see what happens. I cut the crusts off and toast ours which makes it taste very similar to ordinary bread.
Oops I appear to have written an essay 
You could always just try probiotics on their own first-see if they help-before changing diet