First, the easy bit. I'm sure they will have been importing coal into Poole for domestic use, so they would need someone to count it to make sure the Geordies (or whoever) weren't ripping them off!
Next a suggestion. If your 16 year old daughter died in childbirth in 1814, would you not be tempted to have the baby baptised as your daughter and name her after her mother?
And to answer your other question, my wife's many times great Aunt had an illegitimate daughter in Parkstone in 1836, when she was 16, and was married before the 1851 census. It looks like she suffered a problem, as she never had any more children, but she lived with her husband, daughter, and later, daughter's husband and children on Brownsea Island until she was widowed in 1871. Her husband is buried there! So having a child was no barrier to later marriage.
If you have been through the registers at Dorchester ( there is also a copy in the Family History Centre at Poole Museum), the DHFS records at Treetops are transcribed from those. I know where to find them on line, so I will look further now your dates seem to be firming up.