I agree with the scepticism expressed by Roland in the comment to your question. A quadratic curve is probably not a very realistic model for drug accumulation.
You can test significance by combining the data and the models. Include an intercept for the difference between the groups, and it's significance can be interpreted.
long <- mydata %>% gather(drug, amount, Drug1, Drug2)
fit <- lm(amount ~ Time * drug, data = long)
This fits a combined model. I left out the quadratic term. You could include that as well. In terms of significance, this shows that the drugs have a significantly different intercept, but the difference in slope is not significant.
lm(formula = amount ~ Time * drug, data = long)
Min 1Q Median 3Q Max
-2.56364 -0.55758 0.00606 1.03636 1.65455
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7333 0.9057 0.810 0.42997
Time 1.1939 0.1460 8.180 4.15e-07 ***
drugDrug2 4.1333 1.2808 3.227 0.00527 **
Time:drugDrug2 0.1758 0.2064 0.851 0.40707
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.326 on 16 degrees of freedom
Multiple R-squared: 0.9347, Adjusted R-squared: 0.9224
F-statistic: 76.32 on 3 and 16 DF, p-value: 1.073e-09
This all depends on the chosen model. For example, if you include a quadratic term, things can work out differently. You should look into using a model that has a kind of "ceiling", logistic growth for example.
Also, if you're interested in growing your understanding, more flexibility and improving predictions, I recommend looking at (hierarchical) bayesian models with
rstanarm for example.