Denise is right about "doble" being redundant in English; I think Taña's reference from Navarro makes the same point. DT means p(a)ediatric diphtheria and tetanus vaccine, and the initials are used in both Spanish and English. This combination is commonly known in Spanish as "doble bacteriana", and exists in two versions, DT (pediatric) and dT or Td (older children and adults). But we don't call it "double" in English. Nor do we call the "triple bacteriana" or the "triple vírica" triple.

"Doble" has nothing to do with the dose; it refers to the fact that this combined vaccine protects against two bacterial infections.

And Joseph is of course right that the correct word to use here is "pediatric", not "children". I spell it "paediatric", because I'm British, but you probably want the American spelling.

I would put "DT (pediatric diphtheria and tetanus)". You could add "toxoids" or "vaccine" but in this context I don't think you need to.

"DT (doble niños) y dT (doble adultos)
Debido a que la tos convulsa es menos severa en los mayores de 7 años, y que el componente pertussis está vinculado a la mayor parte de los efectos adversos, este componente se suspende en los mayores de esta edad, y así se obtiene la vacuna doble, que previene la difteria y el tétanos.
Existen dos tipos de vacunas:
» Doble niños (DT): utilizada hasta cumplir 7 años de edad en los chicos en que esté contraindicada la vacunación con pertussis.
» Doble adultos (dT): utilizada en los niños de 7 años y mayores, para el refuerzo cada 10 años o para comenzar el esquema en los vacunados previamente."
http://www.farmaciastkl.com/info/vacunas_v_dpt.htm

"Vaccines to Prevent Diphtheria
DTaP: Pediatric diphtheria, tetanus, and acellular pertussis (whooping cough) vaccine (SpanishSite exit disclaimer) (PDF - 141KB)
DT: Pediatric diphtheria and tetanus vaccine
Td: Older children and adults tetanus and diphtheria vaccine (SpanishSite exit disclaimer) (PDF - 287KB)
Tdap: Older children and adults tetanus, diphtheria, and acellular pertussis (whooping cough) vaccine (SpanishSite exit disclaimer) (PDF - 288KB)"
https://www.vaccines.gov/diseases/diphtheria/index.html