Strabane is where 3 civil parishes meet, so you would probably have to check all of the records. Many RC parishes have different names to the Church of Ireland/civil ones. Makes it just a little more confusing. Camus Church of Ireland has records from 1803. The RC records (Clonleigh RC parish) cover 1773 – 95, 1836 & 1837 and 1853 onwards. So no use to you.
Urney COI has churches in Castlederg (records from 1807), Sion Mills (1853) and Urney (1813). Urney RC start in 1866.
Leckpatrick COI has nothing before 1877 (earlier records lost in the 1922 fire in Dublin). Leckpatrick RC is Donagheady (records from 1863 only).
So none of the RC records covers 1832. You have to hope Rebecca was baptised in the Church of Ireland. All of the surviving COI records I have listed have been copied and are in PRONI (the public record office) in Belfast. They are not on-line there so you would need to get someone to look them up for you.
Weaving was indeed a cottage industry. Everyone did it. It’s what the agricultural labourer and his family did when there was no labouring work eg in the winter months. Labourers are notoriously hard to trace because they tended to move around to follow the work. And they generally weren’t listed in the tithes because they didn’t have any land. Farmers were much more obliging. They often stayed in the one place and show up in more land records.
You ask what they wove. The main thing was linen (Irish linen being fairly famous as you probably know) but in earlier times they wove cotton (from raw cotton imported from the USA). That stopped with the US war of independence, and they switched to linen (flax grows in Ireland but the climate is too cold for cotton). They also wove cambric and other materials. It was done on a hand loom weaving machine which you took with you if you moved. (Harris Tweed is still made on the same sort of weaving machine, in the Outer Hebrides, in Scotland). Towards the middle part of the 1800s, mechanized weaving factories started to appear across Ulster. They produced better quality linen, much more quickly than hand weaving could achieve, and so the home weaving industry gradually died out.
Home weaving gave the average Ulster labourer a little cash income (in a society that was largely barter based) and this meant that they were slightly better off than labourers in the rest of Ireland. It also helped ease things for them slightly during the famine. The death rate in Ulster in the 1840s famine was significantly lower than in the rest of Ireland.
