I don't think "domain" is the right level of classification
This won't specifically answer your question, but as you've posed it I think my answer will be more useful than a flat "no".
At its most basic, classification is a story about ancestry. When properly done, a monophyletic clade includes all living and extinct descendants of a given organism. You must have gone to high school rather recently- the 3-domain system has only been around for 40 years, and was only widely accepted in 1990, according to Wikipedia. Previously, Monera was popular, which came after the five-kingdom model, which came after the three kingdom model... etc. Essentially, whenever we've found something suitably ~weird~ it causes a reshuffling of the ancestry story based on the new information.
Finding life on another planet definitely counts as suitably weird. There are a couple ways that this could happen, and how it did will be the deciding factor about how to classify things.
The panspermia hypothesis is correct
Life arose independently
Life was sent from one planet to the other
The panspermia hypothesis
In this proposal, life is scattered throughout the universe and both planets have been arbitrarily "seeded" with life. If this is the case, then the ancestor of your Duotorusa is most closely related to our LUCA. This system would require the introduction of a new, higher classification level- one that includes the planet of origin in its classification, for example. To place Duotorusa at a domain level within our current binomial system would require that Archaea, Bacteria, and Eukarya ALL were seeded separately.
Life arose independently on both planets
This is another possibility. However, we run into the same problem as above- in order to properly create monophyletic clades, we'd need to include a new, higher-level classification domain. Since your Duotorusa's ancestor and our LUCA are comparable, Duotorusa's classification as a domain is misplaced, since it doesn't share a common ancestor with our LUCA.
Life was sent from one to the other
Here's where things get interesting. If some poor extremophile microbe was blasted to another planet, then all life on one planet would fit within the tree of the other. For all we know, we're all the descendants of one Duotorusa and should fit our domains within their domains. Similarly, if Duotorusa was truly a contaminant from the human spacecraft (serves them right) or otherwise from Earth, only then would it be classified under Bacteria. We would never try to shoehorn an alien organism into a category that it clearly doesn't share a common ancestor with.
I drew out some trees:
Basically, your new domain shouldn't be within any known framework. We'd need to come up with a new system if we found life outside the solar system.