Hi Sean
You should be able to move on quite well with your research based on the information you've already got.
First off, apply for a copy of the marriage registration from the General Register Office in Roscommon. It costs 6Euros for a photocopy. Their website is
www.groireland.ie and you'll find an application form there. Unfortunately they don't have an online facility but you can send the form with your credit card number. Fill in the form with the names of Thomas and his bride, the date of the marriage (as close as possible) and the location of Leighlinbridge. They shouldn't have any trouble finding the registration (but bear in mind that they'll charge you 4Euros for their time if they can't locate it).
They'll take up to six weeks to send you a photocopy of the certificate. The information will include Thomas White's occupation, age (although it's also quite likely to say only that he's of Full Age, meaning 21+) and townland address. It will also show the names of the fathers of both bride and groom.
Civil Registration started in 1864 so you may also be able to find Anne Fitzgerald's birth certificate, and that for Thomas if you can pin down his place of birth. The 1901 and 1911 censuses will help you with that. Records for Leighlinbridge are not yet online but should be within the next year.
These websites may help you:
http://www.familysearch.org (check out the IGI)
http://www.census.nationalarchives.ie/about/futureplans.htmlGood luck with your research.
Rose