"I will support you with that."
Translation:Ich werde dich dabei unterstützen.
Yes it is. Literally this would mean "That I will support you", whereas it should be "I will support you with that". If anything, you'd have to use "Damit". But Unterstützen goes with "bei etwas", so "Dabei" is the right choice here.
"Bei dem" works, but sounds wooden. The normal way of saying it is "Dabei". "Bei dem" would only work well if you wanted to stress that you will support the person with THAT thing, but not with something else.