The best first step is probably to locate a marriage cert for Patrick and Bridgid. The census form states that they were married 19 years, which means about 1892. Your can search the
Irish Civil Index for possible marriages... I'd start with Bridgid as Peppard is a quite rare surname, making the search easier. I see a few possible matches, but none in the registration district that would fit with Lusk (i.e. Balrothery).
Name: Bridget Peppard
Registration district: Dublin South
Record type: Marriage
Quarter and year: Oct - Dec 1892
Volume: 2 / Page: 627
Name: Bridget Peppard
Registration district: Dublin North
Record type: Marriage
Quarter and year: Apr - Jun 1888
Volume: 2 / Page: 503
Neither fit the date and location exactly - the closest to the date is the one in Dublin South, but the 1888 marriage would be nearer to the north County Dublin area.
I'll have a look and see if I can find a match for a Patrick Doyle for either of these.
You could also confirm the family details by ordering a cert for one of the children - this would show fathers occupation, mothers maiden name etc. There's a good match in the index for one of the children's births :
Name: Nicholas Doyle
Registration district: Balrothery
Record type: MARRIAGES
Quarter and year: Oct - Dec 1907
Volume: 2 / Page: 389 Name: Nicholas Doyle
Registration district: Balrothery
Record type: BIRTHS
Quarter and year: Oct - Dec 1906
Volume: 2 / Page: 334
Shane
edit - post corrected, I had posted a marriage reference for a Nicholas by mistake.