Just read the 'will you be my guarantor' part too?
Answer = No!!!
I have a friend who works as a bailiff and he spends an astonishingly large proportion of his time working for amigoloans collecting money for the company from guarantors whose 'friends' (often family) have repeatedly failed to make monthly payments and 9 times out of 10 have gone on to vanish.... the company don't care, they get their money plus fees/fines back from guarantors.
If the guarantor won't/can't cough up on the spot (often many, many thousands), they then have 2 men wandering round their home literally working out what's worth £ and what's not.. and taking it away there and then..together with the car.
Your daughter doesn't need a 'gaurantor'... she needs £500 as a deposit and a month's rent upfront for renting a room in a shared house. If you act as 'gaurantor' for a 1 bed flat, you 'guarantee' at least a 6 month tenancy, all fees paid, the works... an utter headache.
You might love her, but her actions since graduating don't say 'mature, reliable, worldly young woman'... they say 'unreliable, naïve, childish.... young woman'...
dare I say a bit spoilt too? 1) Puppy... 2) June was a long time ago.... 3) wanting own home 4) doesn't sound very pleasant towards you 5) clearly doesn't respect your need to lead a happy life with your other half...
A few years ago Mr Wonga would have been the next pickle in her world... now it'll be Mr Amigo (but that'll be a pickle in your world)
Your answer is very simple: No. Non. Pas de my problemo