This house rule really only changes two not particularly powerful spells and is unlikely to unbalance anything

This house rule would only change anything when the character casts a bonus action cantrip spell. Searching on donjon I can only find two such spells, shillelagh and magic stone. Both spells give the caster a weapon to use so without spending the casters action to use it they aren't getting much out of the spell. Based on how limited the spells affected are I don't believe this change would unbalance anything or even come up that often.

Quickening doesn't change anything since the cost to quicken a non-cantrip spell is the same

As @MrNattious pointed out the cost to quicken a non-cantrip spell is the same as the cost to quicken a cantrip. Under the normal rule you could cast any full-action cantrip and whatever quickened spell (be it cantrip or non-cantrip) you wanted along side it. With this house rule you could quicken the full-action cantrip and cast the other spell a a full-action to get the same result. There is no change.

Yes, it is unbalanced.

The proposed cantrip is far superior to an existing leveled spell: Expeditious Retreat.

There are other arguments, based primarily on what you can do on subsequent rounds. Those arguments involve a large number of build variables - specific spell slots, multi-classing, etc. - too many to accurately assess them all. However, they pale in comparison to two empirical facts:

1. The proposed cantrip does not require a spell slot - it can be cast repeatedly without cost.
2. The propose cantrip does not require concentration - it has no chance of being disrupted by damage, losing spent resources.

There's an established precedent with bonus action cantrips. The only other bonus action cantrips - Magic Stone and Shillelagh - both require an action to make effective use of the effect generated by the casting (an attack, in both cases). Making the proposed cantrip a bonus action and have it take effect immediately makes it better than most cantrips, too.