It’s The Cloud Chamber by Howard L. Myers (Ballantine/Del Rey, 1977 — expanded from a shorter version that appeared in Analog in 1969).

Why it matches your memories

1. Earth has become a lifetime penal colony.
   • After the old Terran Empire lost a war with the “League,” the victors quarantined Earth behind an impenetrable energy screen and use it only as a dumping ground for convicts.
   • A single space-field in the foothills of the Rockies is the one legal landing place; freighters touch down now and then to barter luxuries for the metals the prisoners mine in the nearby mountains.

2. The protagonist arrives as a new “criminal.”
   • The story opens with the League ship setting down and unloading a batch of convicts.
   • The point-of-view character is really League Intelligence agent Rake Thompson (name varies in the magazine version). His crime and sentence are a fabrication; he has been planted to find out how the Terrans keep getting forbidden high-tech equipment and to stop any attempt to break the quarantine.

3. A pushy thirteen-/fourteen-year-old girl attaches herself to him.
   • Her name is Lylah (also Layla in the serial). She is precocious, cocky, and delighted to show the newcomer how things work on Earth.

4. The girl has a latent psychic talent.
   • Many Earthborn youngsters have begun to develop “resonance,” a poorly understood parapsychological ability. Lylah’s talent becomes important as the plot unfolds.

5. Hidden agenda.
   • Thompson’s undercover mission is concealed from everyone (including the reader at first). He plays the role of ordinary tough ex-soldier while collecting information.

6. Conspiracy at the spaceport.
   • A local boss is secretly dealing with off-schedule, non-League traders who slip through the blockade. The scheme will give the Earth exiles their own starship and the means to restart the old Empire.
   • Thompson, with Lylah’s help, wrecks the plan, exposes the ringleader, and captures the pirate vessel.

7. Short, fast adventure.
   • The Dell/Del Rey hardcover runs a little over 180 pages and rattles along without digressions.

8. The “try it again in five years” scene.
   • In the wrap-up, Lylah teases Thompson once too often; he tackles her, gives her a single quick kiss, then releases her with the line (paraphrasing), “Come back when you’re legal—say, five years.” She laughs; he boards the commandeered ship for debriefing, leaving open the promise of a future reunion.

9. Stand-alone.
   • The novel ends there; Myers never wrote a sequel.

Everything you listed—the isolated Rocky-Mountain spaceport, the mining economy, the psychic adolescent, the undercover operative, the thwarted clandestine starship deal, and the final playful/gruff farewell—appears exactly in The Cloud Chamber.