Hi,
The scanned baptism record from the parish books is on findmypast Under Robert ( not Roberts)
As you are in the US, It may be far easier ( and cheaper) for you to purchase the copy off there than to contact the record office for exactly the same copy.
Place of marriage is St Elli Llanelli.
I've taken a look at the entry ,it doesn't give the age of the child being baptised, parents and date are the same as on the IG, father was a collier.
http://www.findmypast.co.uk/search/parish-records/baptisms?tab=1If you put in William Robert , exact date of 1838 and llanelli - you'll come across the entry , it will cost 20 credits to view the image ( you can purchase 60 credits for 6 pounds 95)
If you know for sure that he was born in 1838, I wouldn't take much notice of the age on the military record. I have a couple of them where I have their official birth certificates and their ages are out by one to two years on their military records
Hope that helps
Kind regards