There aren't any options at level 3
There's a few options that seem like they might work, but they won't quite do the trick
Comprehend Languages won't work because it only affects the caster (and does not translate for the caster)
So the Sorcerer and Wizard could learn Comprehend Languages to at least understand what the dragon is saying, but they wouldn't be able to reply in kind; they'd have to speak to the Paladin in Common and have the Paladin talk back to the Dragon.
Helm of Comprehending Languages has the same problem
The Helm of Comprehending Languages is an Uncommon Minor Magic Item. A permissive DM might allow you to obtain enough of these (it is a Minor Magic Item, after all) for the whole party to understand the Dragon; but you'd still have the aforementioned problem that only the Paladin could reply to the Dragon.
At Level 5, Tongues becomes an option
The spell Tongues solves this problem far more effectively, even if only for a few hours a day:
This spell grants the creature you touch the ability to understand any spoken language it hears. Moreover, when the target speaks, any creature that knows at least one language and can hear the target understands what it says.
—Tongues, Player's Handbook, 283
After this spell becomes available, you would only need your Cleric (or the Wizard or Sorcerer if they want to choose the spell as a known spell) to cast Tongues on the Dragon, and for an hour at a time, the whole party would both understand what the Dragon is saying, and also be able to speak to the Dragon and have the Dragon understand them.
With the DM's cooperation: Teach the Faerie Dragon how to speak Common
Faerie Dragons have an Intelligence score of 14, meaning they ought to be relatively adept at learning new things. At your DM's behest, you could teach them Common over the course of 8 weeks of downtime:
Given enough free time and the services of an instructor, a character can learn a language or pick up proficiency with a tool.
Resources. Receiving training in a language or tool typically takes at least ten workweeks, but this time is reduced by a number of workweeks equal to the character's Intelligence modifier (an Intelligence penalty doesn't increase the time needed). Training costs 25 gp per workweek.
—Downtime Revisited, Xanathar's Guide to Everything, pg. 134
Treating the Faerie Dragon as though it were a character in its own right, and treating the four party members combined as a single instructor, the Faerie Dragon ought to be able to learn how to speak Common given enough time spent with the party.
Of course, the DM is not required to use PC rules for NPCs, and this rule is considered an Optional rule, so this will require the DM to agree that this is an appropriate use of these rules. As DM personally, I think this is a valid use of these rules.
You could also use the language training rules found in the Player's Handbook if your DM does not like the Xanathar's Guide to Everything revision of those rules, although it would still require the DM agreeing that it's appropriate for an NPC to use these rules. If so, the training would take approximately 35 weeks.
You can spend time between adventures learning a new language or training with a set of tools. Your DM might allow additional training options.
First, you must find an instructor willing to teach you. The DM determines how long it takes, and whether one or more ability checks are required.
The training lasts for 250 days and costs 1 gp per day. After you spend the requisite amount of time and money, you learn the new language or gain proficiency with the new tool.
—Training, Player's Handbook, pg. 187