Not immediately, I've got a massive backlog. How are the other games on the DS? I feel like trips are a good opportunity to start playing.
For the DS games/remakes:
*Like Winter said you can't go wrong with DQ4, it's a classic and easily among the most popular entries in the series mostly due to introducing a fan favourite protagonist and a fan favourite antagonist as well as a few memorable set pieces. There's also a well known story from years ago of a Japanese salaryman attempting to kill his colleague for not agreeing DQ4 was the best DQ game (If there was any doubt about the cultural impact of DQ in Japan).
*DQ6 is my personal favourite outta the Zenithian trilogy but it's also the most difficult, with the early to mid game having a notorious difficulty spike so I would only recommend it if you don't mind a more archaic JRPG. Also some choices really do matter and I think it's the first game where the DQ cosmology actually gets alluded to, so it's a pretty big game overall that does ask a lot from the player but personally I find DQ6 very rewarding to play.
*DQ9 is a oddball since pretty much all the characters in your party (including the MC) are fully customisable which means each cartridge of DQ9 will have different looking party members plus this was the first mainline DQ game to have true multiplayer (local co-op) where you could hop into each other's worlds. Unfortunately outside the MC, the party members are complete blank slates in terms of personality and don't even appear in the cutscenes (iirc) so it's up to the player to characterize them also a ton of postgame content/free DLC is no longer available due to being tied to
dead Nintendo Wi-Fi (including additional missions and lore), honestly DQ9 is probably the DQ game that needs a remake the most with online co-op and the DLC being restored but that's just my take, it's a inoffensive fun casual JRPG overall (in it's current state).
3DS games/remakes:
*DQ7 is considered by some to be the black sheep of the franchise as it marked an end of DQ games coming in a trilogy, that shared a world and overarching themes and instead was the first truly standalone mainline title (iirc). DQ7 is a much more slow paced and methodical game that introduces more puzzle elements into the gameplay where the purpose is not to explore the world but to actually have a world to explore, as a result the early to mid game can be off-putting for some but the game does very much come through in the end imo. DQ7 is kinda an experimental JRPG that might appeal to some more than others.
*DQ8 was pretty much the most beginner friendly entry before DQ11 came out, keeping the traditional spirit of the franchise while introducing some much needed quality of a life improvements also this was the last mainline entry to have recruitable Monsters, so if you enjoyed that feature take full advantage of it here. DQ8 was also the first mainline entry to have voice acting which was a major deal back when it was originally released, so it may help with narrative immersion more also it has the among the most popular soundtracks in the franchise, an overall great JRPG.