Would a Yellow Faerie Dragon be too much for a Chain Familiar? It is CR 1, tiny, and on par with the imp and quasit.

Faerie Dragon - Yellow (dragon)
AC 15  HP 14 (4d4 + 4)  Speed: 10ft., fly 60ft.
Str 3(-4), Dex 20(+5), Con 13(+1)
Wis 12(+1), Int 14(+2), Cha 16(+3)
Skills: Arcana +4, Perception +3, Stealth +7
Senses: darkvision 60 ft., passive perception 13
Languages: Draconic, Sylvan
*Traits
Superior Invisibility: (Concentration-Bonus Action) at-will invisibility
Limited Telepathy.: Telepathically communicate with any other faerie dragon within 60 ft.
Magic Resistance: Advantage on saves against spells and magical effects.
*Actions
Bite: Melee Weapon Attack: +7 attack, 1 Piercing damage,  reach 5 ft.
Euphoria Breath: Recharge 5+, 5 ft., duration 1 minute, Wisdom save (DC 11), or the target can't take reactions and must roll a d6 at the start of each of its turns to determine its behavior during the turn:
1–4. No A or BA, full move in random direction
5–6. No A or BA , can only make a WIS save to break free
Innate Spellcasting: 1/day: color spray, dancing lights, mage hand, minor illusion, mirror image

Yeah, the spell casting might be too much. Mirror image on a familiar? 

if it was modified to be more utilitarian by reducing the DEX to 18, 3 hit die instead of 4, remove mirror image and color spray as a red faerie dragon would have. Its only offense would be the Euphoria Breath which is not as combative as 2 eye beams every round like a gazer.

Unless there is some other ideas for in line balancing with the other CR 1 familiars?

Gazer isn't eligible for the familiar spells either, the only two CR1 creatures that are by the rules are the Imp and Quasit, and even then only to a Pact of Chain Warlock. So maybe your DM is using house rules, in which case they might let you get away with it, but then you'd need to clear it with them.

I know the spell states those specific creatures, but I was just investigating other options. A lot of people have implemented the Gazer as a chainlock familiar for GOO pact warlocks. The faerie dragon is just more appealing as a familiar than the pseudodragon for a character I am building. I am drafting a dragonborn feylock that focuses on whimsy and being lighthearted in all situations no matter how dire. I could just reskin on of the existing stat blocks I guess.