Greetings,
I think that the Order selection panel and UI may be doing a bit of a disservice here communicating what all is actually part of the Druid Dediction given that is provides the full Order description instead of having a special format of it that carves out things that are/aren't provided by the Dedication.
You see, the Druid Dedication does provide you with an Order and some other benefits but it doesn't actually provide everything the full Druid Order would to an actual Druid.
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https://2e.aonprd.com/Feats.aspx?ID=701)
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You cast spells like a druid. You gain access to the Cast a Spell activity. You can prepare two common cantrips each day from the primal spell list in this book or any other primal cantrips you learn or discover. You're trained in spell attack rolls and spell DCs for primal spells. Your key spellcasting ability for druid archetype spells is Wisdom, and they are primal druid spells.
You learn the Druidic language, and you are bound by the druid's anathema.
Choose a druidic order. You become a member of that order and are also bound by its specific anathema, allowing you to take the order's feats. You become trained in Nature and your order's associated skill; for each of these skills in which you were already trained, you become trained in a skill of your choice. You don't gain any other abilities from your choice of order.
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In summary, what you're seeing is correct, the Druid Dedication does not grant an Animal Companion, instead, you'd need to wait a bit until you reach level 4 and then add Basic Wilding which would then grant you a table to select a level 1 or 2 Druid Class Feat which can then be spent on your desired Animal Companion feature.