This cartoon was also aired in Israel, in a similar TV program to "Glub Glub" called "Train of Surprises" (Hebrew: "רכבת ההפתעות", "Rakevet haHafta'ot"). Here, it was given the title "The Dog Bomil" (Hebrew: "הכלב בומיל", "HaKelev Bomil").
Its original German title is "Der Hund Bohumil", produced in the '70s in West Germany (at the time) by Studio Hamburg, and was originally aired in the West German version of the children's bedtime TV program "Sandman" (German: Sandmännchen). In fact, the West German Sandman character makes an appearance in the middle of the first episode you linked to (also at the end).
However, there is no opening and ending in them. Frustrated, I kept searching and found a Korean blog, with its blogger embedded the first 4 episodes from another video source in the blog - this time with an opening and ending! (which I compiled together and uploaded to the link above).
So, the series is 12-episode Italian-produced in 1993. Created and directed by Gianni Boni with a team of animators under the collective name "Gruppo l'Arca di Noe'" ("L'Arca di Noe'" is also the name of the production itself). The main characters are, of course, the young fella Tete' (could also be written as Tetè, if I'm not wrong), and Clodoveo (judging by the masculine name, I think he might be a male in the original Italian version, but could have been exported as a female named Claudia when distributed to other countries such as Israel and South Korea), Tete''s dinosaur expert and guide all along the way.
Seems that it is completely wiped out from the Italian memory (or the Italian web, at least). No mention of it whatsoever. Boni is also known for another series which might say nothing to many of you - "Zig & Zag e i Loro Perche''" (Zig & Zag Wonder Why), but this one is somewhat documented under Boni's name.
Anyway, thank you there very much for trying to help me to find this series! Much appreciation to all of you!
Update: Okay, there's 13 episodes after all. The last episode where they suppose to witness the dinosaurs' extinction is missing from the Korean YouTube playlist.
I took this brief clip from a Israeli video advertisement promoting various children's shows available on VHS. The tapes were released in a series called "Chaverim Metzuyarim" (Hebrew: חברים מצויירים, lit.: "Animated Friends"). Here's the particular point I took it from: youtu.be/apflzfsK6CU?t=4m11s
The VHS was indeed released, but only the cover illustration was, of course, related to this mysterious Gulliver, while the actual Gulliver inside was Saban's...
gulliverlover @ I believe you familiar with most of them, but here are some of the Japanese adaptations: