Quickmail limits the number of initial emails sent per day depending on the account subscription:
Trial Accounts - 100 initial emails per day
Basic Accounts - 200 initial emails per day
Pro Accounts - 500 initial emails per day
Both of these limits are for the entire account, not on a per-Inbox basis. Those limits are to protect the system from abuse by spammers, which can have negative effects on all QuickMail users.
Follow-up emails don't count against the daily initial email limit. That said, Google's daily threshold limit applies to all emails sent from your G Suite account, so it's important to be mindful of the volume of Follow-Ups you're sending. More information about those limits can be found here: https://support.google.com/a/answer/166852?hl=en