No, there is not an exact equivalent, as far as I'm aware. The TLG is a real treasure and Latin would definitely benefit from a sister site.
The closest thing is probably PHI Latin Texts, which has a comprehensive database of Latin literary texts, with the big exception of Christian texts. They also stop earlier than the TLG does. Still, it's a searchable database and uses good quality editions, too.
For Tertullian, though, you'll have to go elsewhere. My suggestion for searching Christian texts is using the "site" function on Google, so site:thelatinlibrary.com "tertullian" "die dominico".
What's really missing with both of these ways is that they you cannot search by lexeme. You'll have to know all the forms of a word yourself and search that way.
Despite the similar name, the Thesaurus Linguae Latinae is not the same as the TLG. Rather, it's a comprehensive dictionary of Latin words. And it's not finished yet, so you can't look up information about resurrectio. But you're in luck! They do reference Tertullian under the dominicus headword, so if you download that PDF you can find the citations. They seem to indicate that it's used to refer to Sunday (as does Lewis and Short), but you can check it out for yourself.
So you can often get what you need with TLL + PHI (or searching TheLatinLibrary), but unfortunately, you'll have to work at it a bit more than you would need to with the TLG.