Quasi-Poisson Regression with non-integer count data

Question

I am trying to run a fixed-effects Poisson Quasi Maximum Likelihood estimator on 3-dimensional(year, country, industry) unbalanced Panel data.

The dependent variable is the number of patents(non-negative and non-integer). The patent data is non-integer because some patents were registered in more than one country and were 'shared' between them.

The main independent variable is deregulation(a dummy variable which equals 0 before the year deregulation was implemented in a country and 1 starting from the implementation year). I am trying to catch the effect of deregulation on patent activity. I also have some independent variables as controls(size and share).

The data looks like this

country          industry  year    pt size_emp  size_val dereg      share id
Austria Food and beverages 1990    NA 59.76742 2844243.5     0 0.10035470  1
Austria Food and beverages 1991 2.023 61.84432 3121737.4     0 0.10254747  1
Austria Food and beverages 1992    NA 61.50290 3724826.9     0 0.11448406  1
Austria Food and beverages 1993 3.344 61.19843 3699648.1     0 0.12175012  1
Austria Food and beverages 1994 6.000 61.83063 3808057.0     0 0.11251291  1
Austria Food and beverages 1995 6.665 17.42631 1073797.4     0 0.11605032  1
Austria Food and beverages 1996 5.020 16.52287 1020846.7     1 0.11730912  1
Austria Food and beverages 1997 7.467 16.84073  811186.0     1 0.10929066  1
Austria Food and beverages 1998 5.433 17.16993  837194.7     1 0.10477675  1
Austria Food and beverages 1999 4.556 17.23248  795350.9     1 0.09516772  1

I want to run quasi-Poisson regression and include year, country, and industry fixed effects. I ran this model

model <- feglm(pt ~ dereg  + log(size_emp) + share|country + industry + year, 
                  data = pdata,cluster = c("country","industry", "year"), 
                  family = quasipoisson) 

The results are as follows

GLM estimation, family = quasipoisson, Dep. Var.: pt
Observations: 4,248 
Fixed-effects: Country: 14,  Industry: 15,  year: 24
Standard-errors: Three-way (Country & Industry & year) 
              Estimate Std. Error  t value Pr(>|t|)    
dereg         0.049263   0.068041 0.724017 0.481882    
log(size_emp) 0.172708   0.070838 2.438100 0.029875 *  
share         3.779300   0.832383 4.540400 0.000555 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
                                           
  Squared Cor.: 0.986039 

My questions are

1. Is quasi-poisson the right model to run in this case? Are the results valid with non-integer data?
2. Is there any other critical issue in the model that I need to pay attention to?

Any help would be much appreciated.