Your physio has just demonstrated her ignorance with regard to DLA.
Your ds sounds very similar to mine, he has SDCP, crawled at 18 months, cruised at 21 months and at 2.9 yrs can walk with a kaye walker but is still way off walking unaided.
You are absolutely entitled to apply for DLA, we were awarded middle rate when ds was 2.3 yrs so should think you would be eligible for at least that also. I also felt slightly fraudulent claiming, however the money is there for people like our children who have different needs and challenges above and beyond other children their age.
The older ds gets the more obvious his differences become and dealing with his mobility becomes harder - its much easier carrying/getting in the car/getting in pushchair etc etc a 19 month old than a 2.9 yro! Whilst my ds's cp is also mild it still has a massive impact on his life/development and ability to access and experience all the things a NT child his age can.
Claiming DLA has certainly eased the financial burden for us, things like clothes and shoes getting worn really quickly and buying a suitable pushchair for him, I am also starting to save for a lycra suit for him as they are not funded by NHS in our area.
Do you see your physio at a child development centre or similar? We do, I was not happy with our first physio for several reasons so spoke to lead physio there and ds was moved onto her caseload instead - I would def consider talking to someone about your physio as she is giving duff advice which could be detrimental - and she could have a detrimental effect on your claim. Also, there is a specialist HV at our CDC who advises on all sorts, I went over my DLA form with her - both she and our physio were v v proactive helping us access all appropriate services/benefits.
We were awarded DLA within 2 weeks of applying, I think this is probably quite quick from reading other threads and don't know whether this was due to whatever i'd written or the support from physio or both.
Good luck with everything.